Papers

The static tidal Love numbers of black holes vanish in general relativity (GR), but are generically non-zero, and in fact 'run' logarithmically with scale, in more general theories or beyond the static limit. We expose a model-agnostic framework for the running of Love numbers at the dynamical level, valid for any tidal perturbation on any static, spherically symmetric, asymptotically flat background, based on the near-zone expansion in powers of the frequency $\omega$ and on the monodromy at spatial infinity. A master recurrence formula determines the monodromy generator to all orders in $\omega^2$, whose three independent entries fully encode the running of the Love numbers. This structure explains the quadratic nature of the renormalization group equation, here proved to all orders and for any type of Love number. We discuss the scheme dependence of the logarithmic coefficients, which is made transparent by the monodromy form. In particular, this clarifies that the anomalous exponents of the tidal field, the so-called 'renormalized angular momentum' of the Mano-Suzuki-Takasugi formalism, are scheme-invariant and directly computable on any spacetime, without need of explicit solutions. We discuss several applications to black holes, including the derivation of a closed-form formula for the leading dynamical running of axial Love numbers of Reissner-Nordström black holes, proving in particular that it vanishes in the extremal limit. For generic black holes beyond GR, we prove that dynamical running probes deformations of the metric at lower multipoles than the static one, and we illustrate the power of the method by deriving some exact results for the Hayward and Bardeen regular black holes.

Dual resonance reconstructs a scattering amplitude from pole expansions in different channels. We propose analytic dual resonance (ADR), requiring that the complete leading pole sum at an integer resonance admit an absolutely convergent local contour integral. ADR yields one-dimensional pairing relations between residues in arbitrary triangulations. Together with an integer planar spectrum, a joint crossing-spin bound, and complex Regge decay permitting unsubtracted reconstruction, these relations uniquely fix the scalar string amplitude for every $n\ge5$. ADR also predicts higher-dimensional pinch relations, which we examine at five and six points. These results connect the analytic structure of dual resonance to the uniqueness of string interactions.

The Wigner function, in general, takes on negative values, and the amount of negativity in the Wigner function gives an operationally meaningful measure of the complexity of simulating the quantum state on a classical computer. In this paper, we study the growth of Wigner negativity of the Hartle-Hawking state of Jackiw-Teitelboim gravity under time evolution. We work in the gravitational length basis, at genus zero, and at high temperature, $\beta \ll 1$. Our main analytic result is simple: to leading order in $\beta$ the state is a Gaussian wavepacket of minimum uncertainty, sitting at rest at the turning point of the Liouville wall. Its Wigner function is therefore positive, and the negativity is $1+\delta(\beta,t)$, where the correction $\delta$ is smaller than any power of $\beta$. We show that $\delta$ is an even function of time, so there is no linear growth at $t=0$, and that once the packet has reflected off the wall its leading-order evolution is a Clifford shear, which cannot change the negativity. We also numerically study the time evolution of the Wigner function and its negativity. We observe that $\delta$ stays below $10^{-11}$ at $t=0$ and through the reflection, then rises slowly over a few tens of $\beta/\pi$, and then approaches a late-time value consistent with $\delta_\infty(\beta) \simeq 0.08\, e^{-4.4/\beta}$ for $0.25 \le \beta \le 1$: the lower the temperature, the larger the late-time negativity. The exact survival amplitude $Z(\beta+it)/Z(\beta)$ fixes the spread complexity to order $t^4$, and it also fixes the seed-normalised Wigner diagnostic of our earlier work (arXiv:2607.04065, arXiv:2607.17346). We take this as evidence that the length basis is ideally suited for a dual, semi-classical description of the dynamics at genus zero. Beyond genus zero the length basis is overcomplete, and we make no statement about finite $e^{S_0}$.

We study spontaneous scalarization of static, spherically symmetric black holes in scalar–Gauss–Bonnet gravity with a Ricci coupling $F=1 \beta\phi^{2}/4+\gamma\beta^{2}\phi^{4}+O(\phi^{6})$ that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in $\beta$, changes sign at $\beta=1.1156$, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to $\gamma$. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as $\gamma$ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.

Antipodal self-duality (ASD) is a remarkable property that relates an amplitude to itself, after performing a suitable kinematic map and reversing the letters of the symbol (more precisely, acting with the antipode of the Hopf algebra of multiple polylogarithms). ASD has been seen in only one process in planar $\mathcal{N}=4$ super-Yang-Mills theory, and its physical origin is unknown, motivating a search for ASD in other contexts. Recently, ASD was found to hold for square fishnet integrals in a strongly-deformed version of planar $\mathcal{N}=4$. In this paper, we investigate the properties of polynomials in ladder integrals under the ASD transformation that leaves the square fishnet invariant. Our basic building blocks are determinants of certain matrices of ladder integrals, that are labeled by partitions or Young diagrams, and automatically obey the Steinmann relations. We employ integrability-based representations of such determinants, which are essentially matrix-model integrals, and the theory of symmetric polynomials to find many more ASD quantities – linear combinations of determinants whose coefficients are expressed using the combinatorics of partitions. As a byproduct, we provide an alternate proof that square fishnet integrals obey ASD.

The study of continuous spin particles, as general low-energy implications of relativity and quantum mechanics, has intensified in recent years with potential experimental signatures. In this note we show that these particles are absent in perturbative super-string theories, generalising a result in arXiv:1302.4771 to the supersymmetric case. This stands out as a general low-energy prediction of all perturbative superstring constructions.

We construct an extensive model of bulk mutual information (MI) in anti-de Sitter spacetime and use it to describe the leading quantum corrections to the MI of certain holographic theories. The equivalence between bulk and boundary MI follows from the Faulkner–Lewkowycz–Maldacena prescription. We show that the extensivity of the bulk MI is sufficient for the quantum-corrected boundary entropy vector to satisfy monogamy of MI and all other holographic entropy cone inequalities. Our model is built from a covariantly conserved current-current kernel in AdS and is realized explicitly by a free massive Dirac fermion, whose boundary MI at long distances is that of a fermionic generalized free field (GFF). The construction also reproduces the expected short-distance divergence structure of a GFF, and the current-current correlator defines a positive and monotonically decreasing function along the renormalization-group flow. We illustrate this explicitly for disjoint half-disks at the conformal fixed point of the model in AdS$_3$, where we present the exact result.

In this work we explores the dynamic solutions of a brane system in a five dimensional space-time under the Hamiltonian perspective, using the De Donner Weyl formalism. We obtain the dynamic equations for the scale factors, and obtain the Friedmann-like equations in general way. We present the solutions of the scale factors as a function of the extra coordinate, $y$, we show that the geometry is related to the matter-energy component in the brane. Finally, we develop the ADM formalism in the brane point of view with the foliation of the 3-dimensional space which is embedded in a 5-dimensional manifold.

The Hamiltonian of a natural quantum system is usually determined indirectly, by proposing microscopic models and comparing their predicted observables with experiment. A more direct approach is to extract information about the Hamiltonian from measurements on the system itself. In many settings, however, direct access to the full system is unavailable and measurements can be performed only through controllable probes, as in quantum sensing and boundary spectroscopy. Existing Hamiltonian learning protocols under such restricted access typically require a special symmetry, a known parametric form, or controlled operations beyond free evolution. We introduce Quantum Krylov Learning (QKL), a restricted-access framework that avoids these requirements. QKL uses single temperature probe autocorrelators and their operator Krylov structure to extract model-independent spectral information about the unknown system. Rather than fitting a parametrized Hamiltonian, it reconstructs the operator Krylov Jacobi matrix representing the dynamical modes accessible to the probe. The method assumes that the unobserved system is at, or near, infinite temperature. Under this condition, the Jacobi matrix can be reconstructed directly from the autocorrelation of a probe observable, without oracle access to the Hamiltonian. The required operations are free evolution under the unknown $H$, together with probe state preparation and measurement. The learning core therefore requires no symmetry, no parametric model, and no controlled-unitary gates. We show a Lieb–Robinson bound for the operator Krylov chain and derive a data-driven criterion for the required observation window. We also establish an end-to-end sample complexity guarantee: under generic conditions on the spectral gaps and weights, the number of measurement shots required to achieve spectral precision $\varepsilon$ is polynomial in $1/\varepsilon$.

The $\hat{Z}$ invariant of a three-manifold $M_{3}$, a half-index of the $3d$ $\mathcal{N}=2$ theory $T[M_{3}]$, is well understood for negative-definite plumbed three-manifolds. For orientation-reversed manifolds, however, the known formulas fail to produce $q$-series, and making sense of the operation $q \rightarrow q^{-1}$ remains a central open problem. Seifert manifolds, whose $\hat{Z}$ invariants are built from false theta functions, offer a natural testing ground. We study “dual false theta functions”, the objects that should replace false theta functions under orientation reversal. Two characterizations of these duals exist in the literature: a modular one, based on mock modularity with a prescribed shadow, and a resurgent one, based on Borel–Mordell integrals and transseries. We prove that the two characterizations are equivalent. We construct a new family of dual false theta functions for values of positive integer $p$ satisfying a Pell-equation condition. Its members are built from Zwegers' indefinite theta functions, have integer coefficients, and have effective central charge $c_{\text{eff}} \leq 1$. We also show that the mock theta functions of Li and Schwagenscheidt satisfy these characterizations and arise from a natural regularization of the divergent product $\eta^{3}(\tau)\psi_{p, a}(- \tau)$.

We numerically find the solutions for slowly moving Schwarzschild black holes in Einstein–aether theory. We use these solutions to compute the sensitivity parameter which describes the coupling of the black hole to the aether field within point-particle effective theory. A simple analytic approximation for the dependence of the sensitivity on the Einstein–aether parameters is derived.

We prove that, for every genus $g\geq 3$, the primary obstruction of each parity component of the moduli superstack of smooth unpunctured super Riemann surfaces is nonzero, both algebraically and holomorphically. Consequently, both components are non-projected and, in particular, non-split: neither admits an algebraic or holomorphic retraction onto its reduced moduli stack of spin curves.

We study gaugino condensates in $\mathcal{N}=1$ $SU(N)$ super-Yang–Mills theory on Eguchi–Hanson space using instanton methods. Fractional topological charge and the spectral asymmetry of the asymptotic $\mathbb{RP}^3$ boundary modify the instanton calculus. A charge-$\frac12$ instanton carries only two adjoint gaugino zero modes and can therefore contribute directly to the bilinear. Because the Eguchi–Hanson path integral prepares a boundary state on $\mathbb{RP}^3$, the observables are boundary-sector-projected amplitudes. Moreover, supersymmetric Ward identities ensure that chiral correlators are independent of insertion points and the Eguchi–Hanson resolution parameter. For $SU(2)$ instanton, with central holonomy, the full collective-coordinate integral gives $\langle\operatorname{tr}(\lambda\lambda)\rangle=16\pi^2\Lambda^3$ for a specified boundary projection, reproducing the flat-space value. For a single $SU(2)$-block embedding in $SU(N>2)$, the noncentral holonomy requires a continuum determinant for renormalization-group invariance, so zero modes alone do not determine the bilinear. We also study a charge-$1$ $SU(4)$ two-block saddle with central holonomy, $16$ bosonic moduli, and $8$ adjoint zero modes. Its collective-coordinate integral gives $\langle\prod_{i=1}^4\operatorname{tr}(\lambda\lambda)(x_i)\rangle=\frac16(16\pi^2\Lambda^3)^4$. Under the assumptions required for position independence and clustering, this result determines the fourth power of the bilinear condensate in the corresponding boundary sector. Since no independent bilinear calculation is available in the same sector, the factor $1/6$ does not by itself constitute a clustering puzzle.

Using fractional anomalous determinants, we construct a model of the trace and axial anomalies of a $SU(3)$ gauge theory at nonzero $\theta$ angle through the couplings to scalar and pseudoscalar glueballs. In the pure gauge theory, we reproduce the $\theta$ dependence of the vacuum energy and the scalar-glueball mass from the lattice, and estimate the jump in the topological charge density for the first-order transition at $\theta = \pi$. In QCD, the coupling of a pseudoscalar glueball to fractional anomalous determinants describes all of the four three-pseudoscalar decay channels of the $0^{-+}$ glueball candidate $X(2370)$ measured by the BESIII collaboration. Measuring the decay rates for $\eta \eta \eta$ and $\eta \eta \eta'$ can provide a stringent test of the model.

BPS decoupling limits of string and M-theory have led to profound insights into gravity and non-perturbative quantum theory, most notably with the AdS/CFT correspondence. In this paper, we initiate the study of twisted BPS decoupling limits, in which the relevant BPS states carry momentum along circle fibers geometrically twisted over a base space. Prime examples are found in type IIB string theory on AdS$_5\times S^5$, for which the twisted limits involve the BPS states of the global symmetry algebra PSU$(2,2|4)$. In general, string fluctuations in a twisted BPS decoupling limit are described by non-relativistic sigma-models on emergent non-Lorentzian target spaces with a natural symplectic structure. This further supports the broader connection between BPS limits and non-Lorentzian geometry. We introduce analogous limits of D-branes as well, probing the same symplectic structure as the string. For AdS$_5\times S^5$, twisted BPS decoupling limits are dual to Spin Matrix theory limits of $\mathcal{N}=4$ supersymmetric Yang-Mills theory, providing tractable and explicit quantum-mechanical descriptions of non-perturbative regimes of AdS/CFT.

In a previous work 2511.21852, we explored the hypothesis that in general theories of quantum gravity, spacetime regions known as generalized entanglement wedges (introduced by Bousso and Penington) have an associated subalgebra of observables in a semiclassical limit. We defined an entropy associated with these subalgebras that obeys the same monotonicity and strong subadditivity properties as the generalized gravitational entropy of generalized entanglement wedges. Here, we test aspects of these ideas making use of tensor network toy models for holography. In this context, the analog of a generalized entanglement wedge is a region for which no region containing it has a smaller number of boundary legs. In the limit of large bond dimension (analogous to the semiclassical limit), we argue that each such region has a canonically associated subalgebra of the full algebra of observables on the boundary Hilbert space, as well as a family of unitarily related von Neumann factor subalgebras. We investigate in detail how various algebraic operations on these subalgebras (e.g. their intersections, joins, and commutants) are related to corresponding geometrical operations on the tensor network regions. We study to what extent the monotonicity and strong subadditivity properties of generalized entropy for generalized entanglement wedges follow from properties of our algebraic entropy. We also introduce an alternative entropic quantity $S(\omega || \omega \circ E_{\mathcal{A}'})$ associated with a subalgebra $\mathcal{A}$ that also obeys monotonicity and strong subadditivity properties with suitable conditions. Finally, we explain how to define a type $II_1$ von Neumann algebra based on an infinite family of random tensor networks with increasing bond dimension such that the regions corresponding to generalized entanglement wedges can be associated with exact subalgebras of this full algebra.

We prove that the classical part of the Nicolai map for a supersymmetric free nonrelativistic particle moving on a Kähler manifold is linear in the Kähler metric and local for its velocity. Moreover, we give an exact expression for the one-loop correction of the map in terms of the Kähler potential and point out a direct way to higher loop order. This provides another example for the rare cases of exact Nicolai maps, and the first all-order one-loop result. As a check we have verified the Nicolai-map conditions to zero and one-loop order (free-action and determinant-matching). A graphical representation is given as well.

At high temperature instantons form a dilute gas, so in QCD-like theories the breaking of the anomalous $U(1)_A$ symmetry is given by integral powers of the anomalous determinant, $\sim (\det \Phi)^{Q}$, where $\Phi\sim \overline{q}_L q_R$ is bilinear in the quark fields, and with untwisted boundary conditions, the topological charge, $Q$, is an integer. A syncretic model is constructed, which is manifestly "beyond Landau". In the chiral limit, at temperatures above the chiral phase transition, $T > T_\chi$, only integral powers of the anomalous determinant appear. Below $T_\chi$, following 't Hooft et al. I assume that the topological charge $Q$ is fractional, as an integer times $1/N_c$, where $N_c$ is the number of colors. I suggest that consequently, fractional powers of the anomalous determinant appear in the chiral effective Lagrangian. For $N_f$ degenerate flavors, this generalizes the Witten-Veneziano term, valid for small $N_f/N_c$, to arbitrary $N_f/N_c$. In this model the chiral phase transition is generically of second order. The two exceptions are for one flavor, where it is probably crossover, and three flavors, where it could well be weakly first order. This can be tested in lattice QCD with $2+1$ flavors by comparing the (known) temperature dependence of the difference of the $\pi^a$ and $a_0^a$ propagators, to the chiral condensate of the strange quark, between $T_\chi$ and $\sim 2 \, T_\chi$. Analogous measurements are possible for one to four degenerate flavors about $T_\chi$. Lastly, I propose an operator for baryon number in the symmetric phase.

Infinite-distance limits play a central role in the Swampland program, but understanding their behaviour at intersections of boundary divisors is subtle, as it requires control over simultaneous limits of several moduli. To address this, we establish a necessary and sufficient criterion for a boundary stratum of arbitrary codimension in the complex-structure moduli space of Calabi-Yau manifolds to lie at infinite Weil-Petersson distance. In particular, intersections of infinite-distance boundary divisors necessarily remain at infinite distance. The result holds for the full Weil-Petersson metric and arbitrary trajectories, including those with unrestricted hierarchies in the saxions and axion winding. In compactifications of Type IIB string theory on Calabi-Yau threefolds, our proof is based on an inequality relating the Weil-Petersson length of a trajectory to the BPS mass associated with an auxiliary charge vector. If this mass tends to zero while the charge-to-mass ratio remains uniformly bounded, every trajectory approaching the limit has infinite length. Using asymptotic Hodge theory, we construct an auxiliary charge vector satisfying these conditions and derive the criterion directly from the limiting mixed Hodge structure associated with the degeneration. More generally, our result applies to polarized variations of Hodge structure of Calabi-Yau type. In particular, we prove Wang's conjecture on finite Weil-Petersson distance for degenerations over higher-dimensional bases.

For a quantum code defined by an isometry $T:H_{\rm code} \to H_{\rm phys}$, an operator map is a *-homomorphism $\varphi: B(H_{\rm code}) \to B(H_{\rm phys})$ from the space of operators on the logical Hilbert space to the space of operators on the physical Hilbert space satisfying $\varphi({\cal O}) T = T {\cal O}$ for every operator ${\cal O}$ on $H_{\rm code}$. This can additionally be taken to be unital $\varphi(I_{code}) = I_{phys}$ if and only if $\dim H_{\rm code}$ divides $\dim H_{\rm phys}$. In this case, $\varphi(B(H_{\rm code})$ is a von Neumann factor subalgebra of $B(H_{\rm phys})$ and we call the pair $(T,\varphi)$ a factor code. A code network is a family of Hilbert spaces $\{{\cal H}_i\}$ indexed by a partially ordered set with isometries $T_{ji}:{\cal H}_i \to {\cal H}_j$ for $i < j$ satisfying $T_{kj} T_{ji} = T_{ki}$ for $i < j < k$. In this paper, we ask when this can be promoted to a factor code network by defining unital operator maps $\varphi_{ji}$ so that $(T_{ji}, \varphi_{ji})$ is a factor code and $\varphi_{kj} \varphi_{ji} = \varphi_{ki}$. We show that the divisibility conditions on Hilbert space dimensions are sufficient for any code network with a tree structure but not in general. For a diamond-shaped network, we show that promotion is possible if and only if the principle angles between $T_{42} H_2$ and $T_{43} H_3$ all have multiplicity divisible by $H_1$. For incomparable $i_1,i_2 < j$, we characterize when $\varphi_{j i_1} (B(H_{i_1}))$ and $\varphi_{j i_2} (B(H_{i_2}))$ commute, when they generate all of $B(H_j)$, and when they intersect only on multiples of the identity. For $i < j_1,j_2 < k$, we characterize when $\varphi_{k j_1} (B(H_{j_1})) \cap \varphi_{k j_2} (B(H_{j_2})) = \varphi_{k i} (B(H_{i}))$ and when these algebras together with $B(H_k)$ form a nondegenerate commuting square.

We derive the necessary and sufficient conditions for AdS$_4$ solutions of $d=11$ supergravity to preserve ${\mathcal{N}} \leq 3$ supersymmetry. We use our setup to first impose ${\mathcal{N}}=2$ supersymmetry, recovering a previously known class of solutions, providing a non-trivial consistency of our equations. We then focus on the ${\mathcal{N}} = 3 $ case, first deriving the Tri-Sasaki class and then proving its uniqueness as the only ${\mathcal{N}} = 3$ AdS$_4$ class in eleven dimensional supergravity. Our work proves that all supersymmetric AdS$_4$ solutions preserving ${\mathcal{N}} > 2 $ supersymmetry are necessarily of Tri-Sasaki type.

As a work selected for the Frontiers of Science Award, we present in the Proceedings of the ICBS an overview of how the techniques from the field of Quantum Information (QI) can be implemented in High-Energy Physics (HEP), including also some novel insights. We focus on the paradigmatic case of the top quark, a drosophila of a relativistic qubit. We study the presence of entanglement, perhaps the most genuine feature of Quantum Mechanics, in top-antitop quark production in high-energy colliders such as the LHC. We also analyze our experimental proposal of a quantum tomography protocol for the top-antitop quark pair, eventually leading to the entanglement observations by the ATLAS and CMS collaborations, which constituted the highest-energy observations of entanglement ever. We discuss how the concepts and techniques developed in our work have effectively spawned an already vast and rich field of QI in HEP.

The global form of the Standard Model (SM) gauge group, $[SU(3)_c\times SU(2)_L\times U(1)_Y]/\Gamma$, with $\Gamma\subseteq\mathbb{Z}_6$, remains undetermined. For $\Gamma=\mathbb{Z}_p$, the SM possesses a residual global electric one-form symmetry $\mathbb{Z}_{6/p}$. Compactification on the thermal circle yields an ordinary discrete zero-form symmetry whose spontaneous breaking can produce cosmological domain walls. We calculate the temperature-dependent tension and width of the $\mathbb{Z}_{6/p}$ domain walls below the electroweak scale, which exist for every quotient except $\Gamma=\mathbb{Z}_6$, finding that their thickness can reach the kilometer scale around reionization in our benchmarks. These macroscopic thermal interfaces, if produced, would constitute the "Great Walls" of the Standard Model. We develop a phenomenological thermal velocity-dependent one-scale model to follow their network evolution, incorporating temperature-dependent surface tension, inertia, and plasma drag. For sufficiently early formation, our benchmarks give an estimated wall energy fraction of order $10^{-14}$ near the onset of Big Bang nucleosynthesis, with further suppression at later times. Uncertainties arise from relating surface free energy to physical wall energy and from late-time plasma evolution and structure formation. Despite their small energy fraction, these walls could probe the global structure of the SM gauge group, motivating dedicated searches for their cosmological signatures.

Neural network field theory specifies a Euclidean field theory by a network architecture and a density on its parameters, so that correlation functions are integrals over those parameters. We introduce constructive neural network field theory and use it to realize finite-volume scalar $\phi^4_2$ as a limit of network measures. For each dyadic momentum shell of the free propagator, the field is given a separate set of neurons with Gaussian coefficients, uniform phases, and frequencies drawn from the shell's spectral density. Once the frequencies and phases are fixed, integrating out one shell's coefficients is a finite-dimensional integral against a Gaussian density reweighted by the Wick-ordered quartic interaction. For widths that grow fast enough with the shell index and almost every draw of the frequencies and phases, the reweighted density is uniformly log-concave for every shell above a threshold, at any coupling in two and three dimensions, and the fluctuations of those shell fields are held to the free-field scale. In two dimensions, an induction over scales shows that shell $j$ contributes $O(2^{-2j}j^3)$ to the log partition function, and the total-variation distance between marginals at successive cutoffs is of the same order. Because these contributions are summable, the ultraviolet cutoff can be removed for any suitable fixed sequence of widths. Almost surely, the ultraviolet and infinite-width limits commute, and in either order the joint laws of finitely many smeared fields converge to those of the standard finite-volume $\phi^4_2$ measure. The method of parametrizing a field via a network organized into momentum shells and integrating out one shell at a time is not specific to $\phi^4_2$, so we expect it to extend to other theories.

We discuss (2+1)d Chern-Simons Higgsing transitions based on conformal embeddings and their relation to the proliferation of anyons. These transitions preserve or enlarge the intrinsic topological order despite reducing the gauge group. When the topological order is enlarged, the two phases differ by anyon condensation, and the transition takes an Abelian topological order to a non-Abelian one. In the $SO(N)_{2} \hookrightarrow SU(N)_{1}$ family with $N \geq 3$, the two semiclassical regimes have equivalent intrinsic topological orders but distinct realizations of a global $U(1)$ symmetry. For odd $N$, these are non-Abelian realizations of transitions from fermionic $1/N$ Laughlin states to charge-$2e$ anyon superconductivity coexisting with the same chiral $\mathbb{Z}_{N}$ topological order. The scalar representations are always non-integrable with respect to the UV Chern-Simons level and therefore do not directly label anyons of the un-Higgsed phase, despite defining Wilson lines in the UV. Using heuristic adjoint screening, we propose candidate anyons in the un-Higgsed phase, while branching under the Higgs subgroup reveals channels corresponding to condensable anyons of the Higgs phase. We further construct a $\mathrm{Spin}(16)_{1} \to \mathrm{Spin}(9)_{2}$ transition admitting a condensable algebra that contains a non-Abelian anyon but not all of the allowed gaugable channels in its self-fusion.

Macrorealism is a fundamental concept in quantum foundations, capturing basic features of our everyday experience. Among the main tools introduced to test violations of macrorealism are the Leggett-Garg inequalities. These inequalities provide necessary and sufficient conditions for a certain data set including the correlators measured in a number of different experimental runs (weak version of macrorealism). Leggett-Garg inequalities have proved useful for detecting violations of macrorealism in neutrino oscillation experiments. However, it is interesting to investigate a set of necessary and sufficient conditions for strong macrorealism - no-signaling-in-time and arrow-of-time conditions - in order to obtain a more complete characterization of macrorealism in the context of neutrino oscillations. In particular, here we extend previous study of the no-signaling-in-time condition to the case of three-flavor neutrino oscillations, including the CP-violating phase of the Pontecorvo-Maki-Nakagawa-Sakata matrix.

We study how AI agents discover and validate scientific formulas using a controlled case study of the hydrotope, a recently discovered geometric formula that combines the different polynomial pieces of nonlinear surface-wave scattering into one global expression. This problem is deceptively difficult: simple formulas can hold within individual frequency regions, but the global result must identify their boundaries and combine exponentially many potentially active terms. We reconstruct how the formula was originally discovered through human–agent collaboration and analyze 18 single-prompt rediscovery runs under no hint and two forms of human guidance: a false hint representing an incorrect prior and a true hint representing domain-informed insight. Only four recover the formula across all kinematic chambers (i.e., regions in which a single polynomial form applies), while most unsuccessful runs find correct chamber polynomials but fail to combine them or test their full domain. Conventional and LLM-assisted symbolic regression and standard machine-learning regressors likewise fail to recover the global formula in our experiments. Guided by these failure modes, we test a PI$+$two-student workflow in which a coordinating lead agent assigns complementary analytic and numerical tasks to two research agents and independently evaluates their results. The PI$+$two-student team successfully rediscovers the complete hydrotope formula, while the same workflow applied to the harder three negative wavenumber problem discovers a new independent verified analytic expression for the six-point amplitude $A_6$.

Starobinsky's original model of inflation, driven by the trace anomaly of conformal fields, and its $R+R^2$ (scalaron) formulation are often treated separately. The original anomaly-driven evolution connects an early de Sitter phase supported by the Euler anomaly to a scalaron regime, where the observable modes leave the horizon. Building on this known background connection, we compute the scalar and tensor spectra on the exact background and find that the anomaly corrections are controlled by $aN_*/(18b)$, where $a$ and $b$ are the Euler-anomaly and $R^2$ coefficients and $N_*$ the number of e-folds after the pivot exits the horizon; scalaron inflation is recovered as this parameter vanishes. The observed tilt at $N_*=60$ then requires only $b/a\simeq35$, rather than the $b/a\gtrsim10^9$ of early realizations. At this benchmark the scalar spectrum is redder than in scalaron inflation at fixed $N_*$, and the tensor-to-scalar ratio is about 17% lower at fixed tilt, a quantitative signature of the anomaly. For minimal gravitational reheating, $N_*\simeq53$, the tilt remains within $1\sigma$ of the Planck value for $b/a\gtrsim35$. In the de Sitter analysis, a finite range of the Weyl coupling excludes an extra real spin-two pole and keeps the causal response decaying. A companion paper gives the full analysis.

Adopting the dimensional-reduction scheme, we diagrammatically compute, at four loops, the beta function of N=2 supersymmetric Yang-Mills theory, which is well known to vanish beyond one loop. This provides a formidable testbed for both the treatment of the problematic $\gamma_5$ Dirac matrix in D dimensions and the implementation of the dimensional-reduction scheme. In the use of the reading-point method of $\gamma_5$, being preferable for convenience, specific details of implementation start to matter at four loops. We thus rigorously validate these implementation issues, which have previously been advocated for the calculation of the gauge-coupling beta functions at four loops in the Standard Model.

We uncover a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations. We study a cubic scalar theory describing a massive particle coupled to massless scalar quanta, which captures the propagator structure relevant to classical scattering in gravity and scalar QED. Using a Schwinger parametrisation of the massive propagators, we compute the classical limit of Magnus amplitudes at tree level in this theory. First, we prove that all hyperclassical contributions cancel at the level of the Schwinger proper-time integrand, before integration. Then, we show that the classical Magnus amplitude precisely matches expectations from worldline quantum field theory. Both results rely on cancellations of disconnected diagrams which we relate to the Hopf algebra, specifically to the action of the adjoint first Eulerian projector, which annihilates the shuffle products associated with disconnected contributions. Moreover, the worldline diagrams include generic directed-tree topologies, whereas the field-theory diagrams only include directed chains. The correspondence we establish between the two therefore leads to a new formula for generic Murua coefficients in terms of simpler directed chain coefficients. Finally, we observe a suggestive connection between Magnus amplitudes and the web-mixing matrices governing the exponentiation of multiple Wilson lines.