Papers

Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.

Entanglement and non-stabilizerness are complementary resources underlying the complexity of quantum states, yet extracting either quantity from large quantum circuits generally requires exponentially scaling resources. In diagrammatic approaches to quantum computation, such as the ZX-calculus, both quantities likewise typically require expensive tensor contractions that are not native to graphical rewriting. Here we show that both entanglement and magic can be efficiently estimated directly from ZX-diagrams. Flow enables efficient extraction of a normal form separating a potentially extensively entangled graph-state backbone from non-Clifford Pauli gadgets. This structure yields additive upper and lower bounds on bipartite entanglement entropy, which we further tighten through a preprocessing procedure that removes or merges redundant non-Clifford contributions. The same normal form gives an upper bound on logarithmic stabilizer extent. We benchmark these methods in random unitary and monitored circuits, and a circuit combining Trotterized Hamiltonian evolution with Clifford layers, finding that the resulting bounds remain informative even at large qubit numbers, circuit depths, and internal spider counts. Our results provide scalable probes of entanglement and non-stabilizerness of ZX-diagrams and establish a bridge between ZX-calculus and quantum many-body resource characterization, with applications across quantum computing, quantum information, and condensed-matter physics.

The recently observed dark matter (DM) nuclear recoil event at an energy of $248 \pm 23\,(\text{stat.}) \pm 23\,(\text{syst.})\,\text{keV}$ at the LUX-ZEPLIN (LZ) experiment, favoring an inelastic scattering interpretation, has motivated various beyond the Standard Model (BSM) scenarios aimed at explaining the observed excess. In particular, this provides an opportunity to probe models that naturally accommodate inelastic DM scattering. In this work, we explore one such possibility by extending the $\rm U(1)_{L_{\mu}-L_{\tau}}$ model with two complex scalar fields, $\Phi$ and $S$, carrying charges $-1$ and $+2$, respectively, under the $\rm U(1)_{L_{\mu}-L_{\tau}}$ gauge symmetry. These charge assignments allow a trilinear interaction between the two scalar fields, which is crucial for generating the DM mass splitting. Following the spontaneous breaking of the $\rm U(1)_{L_{\mu}-L_{\tau}}$ symmetry, with $S$ acquiring a vacuum expectation value and generating a mass for the BSM gauge boson $Z_{\mu\tau}$, the real and imaginary components of $\Phi$ acquire a mass splitting. This naturally gives rise to an inelastic DM scattering scenario that can accommodate the LZ excess. We perform a likelihood-based assessment of the sensitivity of the model parameters to the observed event while consistently accounting for other relevant phenomenological constraints. Finally, we discuss the prospects for probing the viable parameter space at future experiments.

Replica symmetry breaking (RSB) is the organizing principle of mean-field spin-glass theory, yet whether a continuous Parisi hierarchy can arise in a genuinely short-range system in finite spatial dimension remains unresolved. Here we introduce a disordered model of $N$-component vector spins on a $D$-dimensional hypercubic lattice, with random matrix couplings on nearest-neighbor links and random tensor couplings on elementary plaquettes. In the large-$N$ limit, the model supports thermodynamically stable one-step, full, and one-full RSB phases, alongside replica-symmetric paramagnetic and ferromagnetic phases. We find that spatial locality constrains these ordered phases through two distinct infrared mechanisms. ($i$) Quenched random anisotropy destroys uniform ferromagnetism for $D\leq4$ through an Imry-Ma mechanism. ($ii$) A continuous Parisi hierarchy gives rise to replica Goldstone modes whose gaplessness is protected by a Ward identity. At leading order in $1/N$, these modes behave as a band of free spin waves, producing infrared-divergent fluctuations in $D\leq2$ and a Mermin-Wagner instability of the continuously broken phase. Remarkably, the Parisi hierarchy also acquires a direct real-space interpretation. For two pure states with mutual overlap $q$, a characteristic length $\xi(q)$ describes how far the differences between their frozen magnetization patterns remain correlated. Throughout a continuous sector of the Parisi hierarchy, $\xi(q)$ is independent of temperature and decreases monotonically with $q$. The ultrametric organization of pure states is therefore accompanied by an ultrametric hierarchy of real-space correlation lengths: states that separate near the root of the Parisi tree differ through long-wavelength frozen patterns, whereas states that separate farther from the root differ only on progressively shorter scales.

We study warped compactifications of eleven-dimensional supergravity on eight-manifolds to Minkowski or AdS vacua preserving $N=1$ supersymmetry in three dimensions. For backgrounds characterised by a local G$_2$ structure, we derive an off-shell real superpotential functional in terms of the internal geometry and fluxes without performing a finite Kaluza-Klein truncation. We obtain this expression in two independent ways: from the dimensional reduction of the gravitino variation and from the reduction of the eleven-dimensional gravitino action. We show that the critical-point equations, together with the vacuum value of the superpotential, are equivalent to the full set of supersymmetry conditions implied by the eleven-dimensional Killing spinor equations. When the local G$_2$ structure enhances to a global Spin(7) structure, our result reduces to the known superpotential for M-theory on Spin(7) manifolds.

AI agents can now conduct real-world cyberattacks, scale up capabilities with the number of agents, and collectively pursue misaligned goals to obtain rewards. Together, these factors raise the risk of a population explosion of misaligned agents: agents could compromise computers and secretly deploy additional agents, creating a self-reinforcing cycle where larger populations develop greater collective cyber capability and expand further. This raises a fundamental question: What determines whether a population of misaligned agents remains contained or takes off into this self-reinforcing cycle? This population-level problem is ecological safety: unlike individual-agent or multi-agent safety with a fixed population, it concerns the dynamics of the population itself. Here, we develop an ecological theory of AI-agent populations based on a population growth equation in which fitness (growth rate) depends on cybersecurity capability. We show that, without collaboration, the population takes off only when individual-agent capability exceeds a critical threshold. With collaboration, however, collective cybersecurity capability increases with population size. This creates a critical population threshold: below it, the population declines; above it, the population takes off, even though individual-agent capability has not changed. In ecology, this phenomenon is known as the strong Allee effect. Because red teaming a small group of agents cannot guarantee ecological safety in larger populations, our theory calls for ecological red teaming and population pacing: gradually deploying larger agent populations in controlled environments, while measuring how cyber capability scales with population size, and estimating the critical population size for takeoff. Capability gains may lower this threshold, requiring re-estimation for each new model generation.

Testing the horizon properties of astrophysical black holes is a central goal of gravitational-wave astronomy. The recently identified Direct Wave (DW), a prompt non-quasinormal component of GW250114, provides a new probe of near-horizon physics. While it remains unclear whether the DW itself carries horizon information, we show that it enables a novel null test of horizon reflectivity. If the remnant is an exotic compact object (ECO) with a partially reflecting surface, inward plunge radiation is reflected and leaks back through the gravitational potential barrier, producing a delayed DW echo whose amplitude is set by the surface reflectivity ($|\mathcal{R}_s|$). We construct the corresponding echo template, normalized by the observed DW, and search for it in quasinormal-mode-filtered data. We find no evidence for an echo ($\ln\mathcal{B}=-2.9$) and obtain the 90% credible bound $|\mathcal{R}_s|<0.06$, corresponding to a reflected energy fraction below $0.4\%$, for surfaces from $0.1\, M_f$ to a Planck length from the would-be horizon. Our method thus turns the prompt ringdown signal into a direct test of horizon reflectivity.

Building a quantum model involves a tradeoff: how complex the circuit should be, and how much training data it needs. Caro et al. show that models with fewer trainable gates need less training data to generalize well. Q-FLAIR shows that a quantum feature-map circuit can be grown gate-by-gate, stopping once further growth stops improving the training loss. We ask whether these two results combine into a predictable scaling law. Does Q-FLAIR's own stopping rule pick larger or smaller circuits as training data grows? Does the resulting generalization behavior track Caro et al.'s bound? We reimplement Q-FLAIR's growth mechanism faithfully, including its analytic reconstruction and exact stopping rule. We run it on full-resolution (784-pixel) MNIST 3-vs-5 classification, at five training-set sizes from N = 2000 to 10000. We then fine-tune each resulting circuit, so we can measure Caro et al.'s notion of active gates, K. We find no predictable relationship between training-set size and the circuit size Q-FLAIR converges to. Circuit size and test accuracy both vary non-monotonically with N, and seed-to-seed variance is nearly as large as any trend across N. The empirical generalization gap never exceeds Caro et al.'s bound in 14 of 15 runs, so the bound holds as a valid guarantee in those runs. But the gap correlates only weakly with the bound's value (r = 0.12). This shows that K does not explain most of the variation we observe. Why a valid guarantee can coexist with such weak predictive power remains an open question, and answering it may be necessary before circuit depth and training data size can be jointly optimized in practice.

The Lyapunov spectrum of a nonlinear recurrent neural network with random asymmetric couplings is calculated in the limit $N\to\infty$. The calculation is based on a finite-$N$ identity that expresses the cumulative distribution of Lyapunov exponents as a response function of the tangent-space dynamics, with the tangent trajectory selected by a minimum-norm condition rather than by an initial condition. A cavity method then determines this response function at large $N$ through a self-consistent single-site problem. This result establishes that the chaos in this network is extensive and gives access to diffeomorphism-invariant properties of the dynamics. This work was done in collaboration with the AI models GPT-6 Astra and Claude Opus 5.5.

In this note we prove in a broad analytic set-up a general result characterizing the asymptotic vanishing of the $L^2$-relaxation time of averages in the presence of a large incompressible drift-like term. The broad analytic set-up is analogous to that of Constantin-Kiselev-Ryzhik-Zlatos '08 or of Coti Zelati-Delgadino-Elgindi '20. A crucial role is played by the singular value gap method of Chatterjee '25, further developed by Eberle-Lörler '26.

We derive a density functional for quark matter with linear confinement interaction, applying the principle of saturation of color interactions. For the saturation parameter $\mu$ the ansatz $\mu=k_F$ is suggested, where for the Fermi momentum $k_F \propto n^{1/3}$ going to zero the Cornell potential is obtained and at finite quark densities $n$ an interaction energy density functional $\propto n^{2/3}$ results.

The global topology of the Universe is a longstanding open question. In this work, we examine the statistical signatures of a positively curved universe with a Friedmann–Lemaitre–Robertson–Walker metric and the topology of a lens space $L(p,q)$. Since these manifolds are generally statistically anisotropic and inhomogeneous, their cosmic microwave background (CMB) covariance matrices contain non-zero off-diagonal entries that depend on observer location. We compute these full harmonic-space covariance matrices for scalar perturbations for arbitrary lens spaces and observer position. Using the Kullback–Leibler divergence, we assess the distinguishability of these spaces from a simply connected three-sphere with the same curvature. The results show that topological signatures can still be significant in a cosmic-variance-limited regime even when the length, $d_{\rm NC}$, of the shortest loop around the Universe through the observer exceeds the diameter, $d_{\rm LSS}$, of the last-scattering surface by up to $10\%$. This distinguishability depends on the curvature, the lens space and the observer position mainly through the ratio $d_{\rm NC}/d_{\rm LSS}$, which is set not only by the curvature radius but also by $p$, $q$ and the observer location. Therefore, for any value of the spatial curvature, however small, there are lens spaces and observer positions for which $0.985\,d_{\rm LSS}<d_{\rm NC}<1.1\,d_{\rm LSS}$. Such observers would find no matched circles in the CMB large enough to have been detected to date, yet the topology would remain potentially discoverable through its statistical signatures.

We study the energy-energy correlator (EEC) in heavy states of four-dimensional $\mathcal N=4$ super Yang–Mills theory in the large-charge 't Hooft limit, in which the dimension $\Delta$ of the heavy operator (or, equivalently, its $R$-charge) is taken to infinity with the effective coupling $\lambda_Q \propto g_{\mathrm{YM}}^2\Delta$ held fixed. The relevant heavy-heavy-light-light four-point correlators are known to all orders in $\lambda_Q$ in this limit. For certain classes of operators, the perturbative series can be resummed to obtain exact finite-coupling expressions. We use these results to determine the corresponding EEC, whose dynamical part can be extracted from a double discontinuity of the four-point correlator. We determine the EEC at finite effective coupling and study its physical behavior as a function of $\lambda_Q$ and the angular separation between the detectors, both at generic angles and in the collinear and back-to-back limits.

Jet taggers built on the Lund declustering tree encode QCD radiation structure in the inputs and process it with graph networks. We ask whether the tree itself can also constrain the computation, and what becomes accessible when it does. For this, we construct a novel quantum-inspired Tree Tensor Network (TTN), where a single tensor core is shared among the internal nodes of the Cambridge/Aachen declustering tree, employing Lund coordinates, and with no particle-identification or detector-level information. The construction is based on a strong prior on the radiation history rather than on the constituents, complementary to compact equivariant taggers. Because the same learned map acts identically at every node, the trained model can be evaluated on truncated trees and its latent space compared across recursions, and used to localise where on the Lund jet plane the Pythia and Herwig jet representations diverge, showing the regions of generator-dependent concentration. The $\chi=8$ model has 4014 trainable parameters against approximately 391,000 for LundNet. We evaluate boosted top tagging and quark/gluon discrimination at particle level on Pythia and Herwig samples, in both native (Pythia$\to$Pythia) and transfer (Pythia$\to$Herwig) configurations. Despite differing in capacity by two orders of magnitude, the TTN reaches native performance close to LundNet in quark/gluon discrimination, slightly underperforming in top tagging, with a similar Pythia-to-Herwig transfer behavior in both tasks. Finally, we show the behavior of the network as a function of the bond dimension, and as a function of the perturbative scale.

Optical tweezer arrays trapping ultracold atoms and molecules are a versatile quantum science platform with broad impact in quantum simulation, quantum computation, and quantum metrology. The polarization dependence of anisotropic vector and tensor light shifts offers a degree of freedom for precise quantum state engineering of trapped particles. Similarly, state-selective operations depend on the polarization of the addressing light through the atom–light coupling strength. Yet, methods for controlling the polarization of individual tweezers or local addressing beams remain an experimental challenge. Here, we demonstrate independent, site-resolved linear polarization rotation across an optical tweezer array by exploiting the local birefringence tunability of a spatial light modulator. Applying this capability to an array of $^{88}\rm{Sr}$ atoms, we homogenize differential light shifts imparted by the 813-nm tweezers to the narrow ${^1{\rm S}_0}\leftrightarrow{^3{\rm P}_1}$ transition, enabling sideband cooling under a magic-angle condition. Furthermore, we show dynamic transport of trapped atoms across distinct polarization zones with high survival and preserved coherence. Finally, we characterize tweezer polarization noise and demonstrate closed-loop stabilization referenced to the atomic transition frequency, reaching mrad-level stability. Our work establishes a technique for manipulating polarization-sensitive atomic and molecular transitions in tweezer architectures, with immediate applications to optical tweezer clocks and multi-zone quantum processors.

Early fault-tolerant quantum algorithms are a key step in scalable quantum computing, but are ultimately constrained by residual, uncorrectable logical errors. Logical quantum error mitigation can eliminate this bias, however its standard requirements include prior noise characterization, more complex experiments, and substantial sampling overhead. Although no mitigation technique can simultaneously overcome all three constraints, we demonstrate that the first two—noise learning and need for modified circuits—can be completely bypassed for logical circuits by leveraging only syndrome records. Specifically, we introduce virtual error cancellation: a method that, unlike previous bias-free approaches, operates entirely in classical post-processing on universal quantum circuits. We develop and numerically test end-to-end protocols that reduce the sampling overhead beyond fundamental limitations of existing syndrome-aware mitigation techniques, including syndrome-based postselection. In particular, we propose a scheme that pairs the low-latency decoder used in the experiment with a high-complexity decoder run in post-processing. In numerical simulations of a distance-7 rotated surface code, we show that our full-stack dual-decoder algorithm exhibits an error that diminishes as the number of samples increases, capable of reaching more than three orders of magnitude of suppression compared to the decoded logical error rate in an experimentally achievable setting. These results establish syndrome records as a resource for correcting universal computational estimates after quantum execution.

JWST has revealed massive star clusters at $z\gtrsim 6$, which provide promising environments for massive black hole (MBH) seed formation. We introduce a new MBH seeding model for cosmological simulations, physically motivated by the runaway collisions in star clusters. Subgrid star clusters are generated according to the local ISM and evolved through stellar evolution and two-body relaxation. The masses of MBH seeds formed through runaway collisions are determined by the properties of their host clusters, including the effects of metallicity-dependent stellar winds. We further follow tidal disruption events (TDEs) with the evolving clusters, which can be enhanced in MBH binaries, and account for gravitational-wave (GW) recoil following MBH mergers. We implement this model in a constrained simulation of a 5$\sigma$ overdense region, where seeds of $10^{3}-10^{5.6}\,M_\odot$ form in clusters with $10^{4}\leq m_{\rm SC}\leq 10^{8}\,M_\odot$. Because both the seed abundance and mass are directly connected to the local environment, we have a more physical $M_{\rm BH}\!-\!M_{\rm galaxy}$ scaling for low-mass galaxies ($M_{\rm galaxy}\sim10^{6-9}\,M_\odot$), a regime poorly described by previous seeding models. Multiple MBHs are naturally allowed to form in-situ within individual halos, producing a spatially clustered population. This increases the MBH merger rate by $\sim100$ relative to other seeding models, significantly enhancing the expected LISA event rate. TDEs can dominate the growth of $10^{3-4}\,M_\odot$ MBHs and produce luminous flares of $L_{\rm peak}\sim 10^{42-43}\,{\rm erg\,s^{-1}}$, increasing the observability of low-mass seeds. This seeding prescription accelerates early MBH growth at $z\gtrsim 8$, while subsequent self-regulated gas accretion drives the central MBH toward similar masses $\sim10^{8.6}\, M_\odot$ by $z=6$ across different seeding models.

We propose a novel numerical method for transport-dominated problems using Physics-Informed Neural Networks (PINNs). In such problems, the solution can develop large gradients and fine structures over time. This is particularly challenging for classical PINNs, which represent the solution itself. In our approach, rather than the solution, we choose to approximate the flow map of the equation. The solution is then recovered by pulling back the exact initial condition, so that its fine structures are produced by the map rather than represented by the network. Our method is constructed by approximating the flow map of the equation with multiple PINNs, one per time subinterval, and composing them using the semigroup property of the flow, so that each network only has to represent a map close to the identity. To highlight the advantages of our method compared to classical PINNs or classical numerical schemes, we present numerical results on the linear advection equation, the incompressible Euler equation in vorticity formulation, the Vlasov-Poisson equation, and finally a drift-kinetic equation.

The star-forming main sequence (SFMS; $M_\star$–sSFR), the gas-to-stellar mass relation ($M_\star$–$M_{\rm gas}/M_\star$), and the mass–metallicity relation (MZR; $M_\star$–$Z_{\rm gas}$) are three core scaling relations for star-forming galaxies, and together they encode the information about the baryon cycle that operates during galaxy evolution. We investigate how these relations emerge by modelling the gas flows that regulate the baryon cycle, using both an ideal and a cosmological gas flow model, and identify a hierarchy among the three relations, with one further parameter entering the scatter budget at each step. In our model, the SFMS and its scatter are set primarily by the formation time of the host halo, with a weak dependence on the star formation efficiency and the mass-loading factor. The gas-to-stellar mass relation follows from the ratio of the sSFR to the star formation efficiency, and inherits the scatter of both. The MZR in turn follows from the gas-to-stellar mass relation together with the mass-loading factor, their relative contributions depending on the galaxy evolutionary state between the inflow-driven regime and equilibrium. This hierarchy naturally introduces further correlations among the three relations, such as the fundamental plane of star formation ($M_\star$–$M_{\rm gas}$–SFR), the fundamental metallicity relation ($M_\star$–SFR–$Z_{\rm gas}$) and its gaseous counterpart ($M_\star$–$M_{\rm gas}$–$Z_{\rm gas}$), and the correlations of each relation with galaxy size, which traces the star formation efficiency through the star formation law. Together, the three core scaling relations and the higher-dimensional correlations among them follow from a single framework, providing a foundation for linking the observables of star-forming galaxies to the underlying baryon cycle.

Gravitational waves from vacuum first-order phase transitions probe the nonlinear dynamics of relativistic bubble collisions. Predicting their spectrum requires resolving Lorentz-contracted scalar bubble walls throughout a volume containing many bubbles, making the large-boost regime prohibitively expensive for direct lattice simulations. We develop a simulation-based pairwise surrogate that separates the microscopic collision dynamics from the geometry of the multi-bubble transition. This utilizes symmetry-reduced $(1+1)$-dimensional scalar-field simulations to build a library of two-bubble gravitational-wave spectra, including the nonlinear post-collision evolution. These spectra are combined with geometric weights that account for screening by other bubbles. We test the two-bubble spectra and the reconstructed spectra of three- and many-bubble systems against full $(3+1)$-dimensional lattice simulations. Not only can the surrogate be orders of magnitude cheaper computationally, but it also provides access to highly relativistic collisions beyond the practical reach of direct many-bubble simulations. This provides a route to studying how the spectral amplitude and shape depend on the collision boost and scalar potential.

We construct a family of self-dual $(1+1)$-dimensional $\mathbb{CP}^1$ sigma models whose potentials $V$ are determined from pre-potentials $U$ by Platonic geometry. Using the round metric on $\mathbb{S}^2\simeq\mathbb{CP}^1$ and the generalized self-duality formalism, we build symmetry-invariant pre-potentials $U$ from the unit vertices of each Platonic solid intersecting the unit circumsphere. The regular-lattice sites associated with vertex, face-center, and edge-midpoint directions are critical points of $U$ and degenerate vacua of the scalar potential $V$. Dual solids share the same regular lattice but generate different pre-potentials, charges, potentials, and metric-gradient flows. Numerical integration reveals distinct self-dual trajectories and energy-density profiles, including multi-peak structures for paths passing near saddle points, while solutions with the same endpoint difference $\Delta U$ have the same total energy. The positive maxima of $V$ are also organized into symmetry orbits. This construction provides a geometric prescription for controlling the vacuum structure and self-dual sectors of $\mathbb{CP}^1$ models with a potential.

We present a generalization of T-duality, called $T_2$-duality, that captures certain aspects of U-duality in M-theory. In particular, it features backgrounds that contain a 2-gerbe over a principal torus bundle, structures familiar from eleven-dimensional supergravity backgrounds. In special cases, it also incorporates S-duality in a precise sense. Our main result is a theorem characterizing $T_2$-dual pairs through spans of categorified principal bundles with connections, giving explicit rules for constructing a $T_2$-dual for a given background. A number of explicit examples illustrate how the various characteristic classes are mapped between the left and right backgrounds. For two-dimensional torus fibers, we also relate our construction to the combination of dimensional reduction and T-duality that links eleven-dimensional supergravity to type IIB supergravity. Finally, we discuss how $T_2$-duality arises from a Buscher-like span of 3d sigma models.

We study how charged-lepton flavour violation (CLFV) generated in the $\tau$ sector propagates into the $\mu\to e$ sector within the Standard Model Effective Field Theory (SMEFT). Assuming that new physics at a scale $\Lambda\gg v$ produces only dimension-6 operators that mediate $\tau\to e$ and $\tau\to\mu$ transitions, we identify and compare the three mechanisms that induce $\mu\to e$ observables. All three originate from double insertions of the two $\tau\to\ell$ operators and scale as $C_6^{\tau e}C_6^{\tau\mu}/\Lambda^4$. (T1) Renormalization-group mixing misaligns the charged-lepton mass matrix, and the rotation to the mass basis generates dimension-6 $\mu\to e$ operators. (T2) A finite, non-logarithmic remainder, which we find to be negligible. (T3) The overall divergence renormalizes dimension-8 operators, contributing after electroweak symmetry breaking. Since T1 and T3 carry no relative power of $\Lambda$, neither can be neglected at any scale, and only their comparison reveals which mechanism, and hence which $\mu\to e$ observable, most strongly probes a given operator pair. Surveying the Warsaw-basis operators, we classify representative $(\tau\to e,\tau\to\mu)$ pairs into T1-dominated, T3-dominated, and T1–T3-comparable regimes, and explain the hierarchy through the underlying mixing chains. Translating current $\mu\to e\gamma$, $\mu\to eee$ and $\mu\to e$ conversion limits into bounds on products of $\tau\to\ell$ Wilson coefficients, we find that they exceed the direct $\tau$-decay constraints by factors of ten to several hundred. Excluding either T1 or T3 would miss these limits by orders of magnitude for some pairs, and shift them by factors of two to three in others. Interpreting $\mu\to e$ data as a probe of $\tau$ flavour violation therefore requires both the dimension-6 RG running and the dimension-8 mixing contributions.

We construct higher-dimensional swirling spacetimes in vacuum General Relativity using the hidden symmetries of the dimensionally reduced theory. Working directly with the coset-space formulation, we perform in five dimensions a reduction along the two independent axial Killing vectors, obtaining an $SL(3,\mathbb{R})/SO(3)$ sigma model and a genuinely five-dimensional background with two independent swirling parameters. The same transformation yields doubly swirling Schwarzschild–Tangherlini and Myers–Perry geometries. A distinctive feature of the new background is its multidirectional asymptotic structure. Correlated radial-angular limits reveal directional curvature singularities that are invisible in the usual large-radius limit at fixed angle. We further exhibit causal geodesics that reach such singular asymptotic ends in finite affine parameter. Finally, we describe the maximally axial extension of this construction to higher dimensions: five dimensions are maximal for an entirely axial reduction to three dimensions, while six dimensions admit an additional nontrivial translational deformation, with further dimensions contributing only flat spectator directions.

While models of undirected and directed geometry in random i.i.d. disorder with rapidly decaying tails are expected to behave similarly and exhibit features of the Kardar–Parisi–Zhang universality class, the scenario when the background noise is fractal is expected to be significantly different. A canonical example of the latter is Liouville Quantum Gravity, where the planar Gaussian free field forms the fractal background. A toy model capturing some of the essential features is given by Mandelbrot's fractal percolation, a random Cantor set. In the simplest setting, dyadic cubes of different scales are retained independently with probability $p$ (a parameter of the model), and the intersection of all retained cubes forms the set of open sites. Connectivity properties of such sets have been intensely studied. Across [CCD88, Cha95], a surprising result was proven. Namely, while there is a phase transition for connectivity of the fractal percolation set (like in usual bond percolation), directed percolation never occurs. Results of a similar spirit have been obtained in geometric measure theory as well. As a step towards understanding last passage percolation (LPP) driven by the Gaussian free field (initiated in [GGN24]), we study the problem of quantifying LPP in fractal percolation. Developing a multi-scale framework, we show an almost polynomial gap from linear growth of the passage time. The obstruction to high LPP values is the Lipschitz nature of directed paths. Along these lines, [Cha96] showed that any connected subset of fractal percolation must have Hausdorff dimension strictly larger than one. We show that one can construct directed paths passing through open sites in fractal percolation provided they move exponentially fast in the spatial direction—a model we introduce and term as unrectifiable directed percolation.

We determine the two-way quantum and secret-key capacities of the pure-loss channel under an average input photon-number constraint. For transmissivity $\eta$ and photon budget $N$, both capacities equal $g(N)-g((1-\eta)N)$, where $g$ is the entropy of a thermal state. This coincides with the rate achieved by the known reverse coherent information of a two-mode squeezed vacuum. Our result provides the last missing capacity formula for the celebrated pure-loss channel, completing the picture of bosonic quantum communication under pure loss.

A newborn neutron star (NS) that survives after a binary NS merger can inject its rotational energy into the surrounding ejecta while the ejecta are still optically thick. The injected energy is redistributed by the pair cascade, and the nebula becomes a radiation-dominated plasma composed of photons and e^+- pairs. Compton scattering then governs the energy exchange while the photon number is conserved in scattering. This nebula is evolved with a one-zone model that includes pair creation, annihilation, photon injection, diffusion, and in particular the leakage through the jet-induced polar funnel. For typical parameters, we find that the Compton parameter y is much larger than unity at early times. The nebula therefore remains in saturated Comptonization for 100 s to a few thousand seconds, depending on the magnetic field strength of the post-merger NS. The radiation field takes a Wien spectrum with a Compton equilibrium temperature. The nebula is then a so-called Wien fireball. The Compton temperature decreases from tens of keV to a few keV at early times. As long as the ejecta are optically thick, the funnel leakage is comparable to or exceeds the adiabatic loss. The funnel emission is quasi-thermal, and its isotropic-equivalent luminosity is much higher than the spin-down luminosity. We suggest that the quasi-thermal components observed in the extended emission of short gamma-ray bursts could come from the funnel leakage of the nebula fireball.

We study two problems: Local Leakage Resilience (LLR) for Shamir secret sharing, and worst-case Optimal Polynomial Intersection (OPI). Both problems concern polynomials $Q(X)$ of degree less than $k$, over a prime-order finite field $\mathbb{F}_p$. In LLR for Shamir secret sharing, one asks how much one can learn about $Q(0)$ given a few bits leaked from each of $Q(\alpha_1), \ldots, Q(\alpha_n)$, for distinct non-zero evaluation points $\alpha_i \in \mathbb{F}_p$. In OPI, one is given input list $S_1, \ldots, S_n \subset \mathbb{F}_p$, and wants to find a polynomial $Q(X)$ of degree less than $k$ so that $Q(\alpha_i) \in S_i$ for as many $i$ as possible. Leveraging recent connection between these two problems due to (Sun, Wootters 2026), we improve the state-of-the-art for both problems. For LLR, we show that there is some constant $\delta > 0$ so that, as long as $R := k/n \geq 1/2 - \delta$, Shamir secret-sharing is one-bit locally leakage resilient (meaning that one can learn only a negligible amount about $Q(0)$). This is the first result to break the so-called "one-half barrier" for LLR, and improves over the previous best known result, requiring $R \geq 0.668$ (Kasser, 2025). For OPI, we give a quantum algorithm that finds a polynomial $Q(X)$ that agrees with at least a $\mathsf{SCL}_\rho(R)-\varepsilon$ fraction of the lists in expectation, for every fixed $\varepsilon>0$, where $\mathsf{SCL}_\rho$ is the semicircle law of (Jordan et al., 2025). This improves previous algorithmic (and existential) results of (Jo, 2026) and (Horinaga, Yamakawa, 2026). We also give further improved existential results. We also adapt the hardness result of (Yamakawa, Zhandry, 2024) to apply to OPI (rather than a folded version); over large fields, this gives an unconditional separation between the quantum and classical hardness of OPI relative to a membership oracle.

Year-scale quasi-periodic oscillations (QPOs) in blazar gamma-ray light curves have been proposed as signatures of supermassive binary black holes and precessing jets. Red noise can mimic periodicity, and detection alone does not establish persistence or period stability. We develop and calibrate a morphological framework to characterize year-scale modulation and constrain the incidence of stable modulation in blazars. We analyze 120 Fermi-LAT light curves spanning 18.1 yr. Singular spectrum analysis selects the oscillatory mode and period, while weighted wavelet Z-transform ridge tracking measures persistence, period drift, and cycle-to-cycle volatility. Flux randomization, 10,000 red-noise simulations, and about 20,000 injections calibrate the classification. Of 97 quality-selected sources, two show persistent, coherent modulation consistent with a stationary period (Rank I: PG 1553+113 and B2 1215+30), six show coherent modulation whose stationarity cannot be established (Rank II), and 89 form Rank III. Neither Rank I nor Rank II significantly exceeds red-noise expectations. Stationary 1-3 yr injections reach Rank I in 63-97% of trials at signal-to-noise ratio (SNR) = 1, depending on period, and 100% at SNR = 2; 92% of drifting injections reach Rank II. These results limit stable, approximately sinusoidal 1-3 yr modulation to at most 7% of the sample at SNR >= 1 and 5% at SNR >= 2 (95% confidence). PG 1553+113 has the lowest false-alarm probability, 4.7% after trials. Stable year-scale modulation is uncommon, and no source is established as periodic. The framework distinguishes persistent, stationary modulation from coherent variability whose period may evolve or fluctuate, but not the physical mechanism. PG 1553+113 and B2 1215+30 are candidates for monitoring and continuous gravitational-wave searches, although their stability does not establish a binary origin.

We develop a framework to construct large decoherence-free subspaces with a non-trivial structure. The construction is based on hybrid quantum systems in which quantum matter is coupled to a dissipative bosonic mode. Dissipation imposes a global constraint on the matter by selecting the matter null states in the long-time limit. The decoherence-free subspaces spanned by matter null states can exhibit exotic quantum properties and emergent symmetries that do not characterize the full Liouvillian dynamics. We show how to construct many-body operators with physically interesting null states by employing representation theory of Lie algebras. This approach allows us to choose models based on their underlying algebraic structure. We consider explicitly the example of coupling a lossy optical cavity to the directed tunneling operator of quantum particles in one-dimension. In this case, the symmetries of the decoherence-free subspace originate in an $\mathfrak{sl}(2,\mathbb{C})$ algebra, leading to an exponentially large number of steady states. We characterize the null states for both fermionic and bosonic particles, employing analytical and numerical methods. The states exhibit several properties that underline their complex quantum nature: long-range kinetic correlations and volume-law entanglement. The nonreciprocal nature of the directed tunneling dynamics leads to the emergence in the many-body regime of a symmetry-constrained Liouvillian skin effect. The open light-matter system exhibits a strong symmetry stemming from spinless $\eta$-pairing algebras. We show how the non-trivial properties of the long-times states emerge in the dissipative dynamics from generic initial states, by performing time-dependent matrix product state simulations. Our framework opens avenues for dissipatively engineering complex quantum correlations and harnessing nonreciprocity in a controlled manner.