Papers

We formulate false-vacuum decay in a mixed-field Ising chain with $1/r^\alpha$ interactions as a spatially nonlocal Euclidean $\phi^4$ theory featuring a fractional spatial kinetic term $\sim |q|^\sigma$, where $\sigma=\alpha-1$. The nonlocal bounce is anisotropic in space-time and develops algebraic spatial tails, challenging the standard thin-wall picture of a compact droplet. Combining thin-wall arguments with numerical solutions of the full nonlocal saddle, we show that these tails preserve the leading thin-wall exponents, manifesting instead in subleading corrections. For $0<\sigma<1$, the lifetime exponent scales with the energy bias $h$ of the metastable state as $B\sim h^{-1/\sigma}$; for $1<\sigma<2$, the leading Coleman scaling $B\sim h^{-1}$ is recovered, while long-range effects are retained in the subdominant term $\sim h^{\sigma-2}$. Our results show that tunable long-range interactions fundamentally reshape bubble nucleation and alter false-vacuum decay in quantum simulators.

In various approaches to quantum gravity, spacetime geometry is understood to emerge from more fundamental discrete structures at the Planck scale. As sometimes posited, their presence could lead to dissipative effects in the smooth effective sector. In this paper, we develop the idea of non-conservation in gravity, by introducing an effective cosmological model within unimodular gravity, in which a varying cosmological constant arises as a consequence of dissipation. We show that this requires to incorporate hidden degrees of freedom – termed quantum gravity defects – that act as an effective bath for the matter fields. To illustrate the viability of the framework, we study the case of an Ohmic bath inspired by the Caldeira-Leggett model for Brownian motion, leading to a diffusion equation for the matter energy density. The results show that, starting from a primordial universe with no dark energy, dissipation can account for the generation of a small positive cosmological constant.

The CMS Collaboration reported a local excess at $146~\mathrm{GeV}$ in the search for the lepton-flavor-violating decay of the Higgs boson and additional Higgs bosons in the $e\mu$ final state at $\sqrt{s}= 13~\mathrm{TeV}$. If confirmed, this would constitute a major piece of evidence of charged lepton flavor violation (cLFV). We investigate the compatibility of the claimed signal with the full suite of existing low-energy cLFV constraints in a bottom-up effective description: a single real scalar of mass $146~\mathrm{GeV}$ coupled to gluons and to all charged-lepton bilinears, with seven free parameters that simultaneously control the LHC production cross section, every di-lepton decay channel, and every low-energy cLFV observable. A Bayesian MCMC analysis against $\mu-e$ conversion, muonium-antimuonium oscillation, three-lepton and radiative LFV decays, semileptonic $\tau$ LFV decays, and LHC di-lepton searches yields a preferred mode with peaked value $Y_{e\mu} \sim 10^{-4.09}$, already cut into by the current $\mu-e$ conversion limits. The projected sensitivities of Mu2e, COMET, Mu3e, MACE, MEG~II, Belle~II, STCF, and the HL-LHC directly probe the region of coupling space selected by the CMS excess, so the complementarity between high-energy and low-energy cLFV probes will either corroborate or decisively exclude the scalar interpretation of the anomaly within the next decade.

The ringdown waves from a black hole offer a clean probe of strong-field gravity, but a matter distribution that may be present around a realistic black hole renders the background spacetime dynamical and the ringdown frequencies time-dependent. We study the odd-parity ringdown of a Schwarzschild black hole that grows through the dilute, steady, spherically symmetric accretion of a perfect fluid. Working to first order in the accretion rate, we compute the ringdown waveform directly in the time domain on this dynamical background. Since the odd-parity matter perturbation decouples from the metric perturbation, the wave mode can be described by a purely tensorial mode on the accreting background. In particular, the ratio of the imaginary to the real part of the frequency cancels both the secular variation caused by the growth of the black hole and the redshift factor, so that its deviation from the Schwarzschild value purely reflects the surrounding environment. The time dependence of the frequency, on the other hand, reflects the accretion rate and allows us to define a second observable tied to it. We argue that measuring these observables across multiple modes may provide significant information to constrain the surrounding environment of the black hole.

We examine the question of whether the discrete transformation CRT is a gauge symmetry of “Quantum Gravity". Since the phrase in quotes is not yet completely well defined, we first try to define specific frameworks in which one might ask the question. We find that the general answer is NO. In asymptotically flat and AdS spaces, CRT is an asymptotic gauge symmetry in the same sense that the continuous parts of the Poincare/AdS isometry groups and scalar internal symmetries are. In eternal dS space it can be considered a spontaneously broken gauge symmetry if a certain “Alice String" configuration is allowed in the Thermofield double Hilbert space. This requires an extension of the conventional Chern-Simons rewriting of $2 + 1$ dimensional gravity. This interpretation only makes sense if we consider the underlying quantum mechanics to be time independent. General quantum measurement and semi-classical gravitational restrictions on measuring devices put a priori limits on the existence of detectors with clocks that can actually measure proper time along a classical dS geodesic.

Supermassive black holes (SMBHs) powering quasars at $z \gtrsim 6$ are difficult to grow from stellar mass remnants, motivating seeds from primordial black holes (PBHs) with masses $10^5-10^7 M_{\odot}$. This range is constrained by the COBE/FIRAS bound on the CMB $\mu$-distortion, which limits the small-scale curvature variance to $\sigma_\zeta^2 \lesssim 10^{-4}$. For Gaussian perturbations, the variance fixes the far tail of the one-point probability distribution function (PDF), making the PBH abundance negligible. We call this the Gaussian barrier. The barrier can be evaded only if the variance probed by the distortion is decoupled from the tail probability controlling collapse. We implement this idea in the non-perturbative $\delta N$ formalism and relate asymptotic PDF tails to the global shape of the $\delta N$ map. Four Gaussian-cored families are analyzed: generalized-normal, stretched-exponential, power-law, and log-normal tails. After standardizing each family to unit variance, we impose the FIRAS cap and compute the distortion-limited PBH abundance in the tail-shape parameter space. The ordinary exponential tail produced by standard single-field non-attractor dynamics is still too light to reopen the seed window. Algebraic tails from fractional-potential dynamics, and sufficiently heavy log-normal tails treated as a phenomenological proxy for multiplicative dynamics, can supply seed-relevant abundances while respecting the distortion bound.

We evaluate exactly the radial metric factor $h(\zeta)$ generated by Schwarzian averaging in the AdS$_2$ throat of an extremal Reissner–Nordström AdS$_5$ black brane. The result is a Gaussian integral against $\coth(\pi y)$, valid at all radial depths, which Mordell's identity turns into an exact Appell–Lerch $q/q^\ast$-series representation. The dual series identifies the nonperturbative scale $e^{-\pi^2 C/\zeta}$ missed by any finite near-boundary truncation. The third parametric derivative required by the evaluation generates the quasimodular Eisenstein series $E_2$, absent from the classical Mordell identity. From the integral representation we prove that $\mathcal{G}_0(\zeta):=h(\zeta)/\zeta^2$ is completely monotone and hence has no interior minimum, so any confining minimum produced by a finite near-boundary truncation is an artifact. We also compute the exact relative variance of the Schwarzian kernel, which makes the averaged-metric approximation error quantitative and shows that the absence of a confining minimum is robust across moment-based effective geometries. Applied to the temporal rectangular Wilson loop, the exact throat gives algebraic screening, $E(L)\sim -\kappa_{\rm IR}/L^2$, the Wilson-loop diagnostic of the semi-local quantum-liquid IR of the extremal RN brane. A numerical check in a simple matched geometry confirms that the screened saddle is the dominant string configuration, and an exact-versus-truncated force comparison shows that the apparent constant-force regime of the fourth-order truncation is not a feature of the exact geometry.

We study a graph classification problem involving over 20 million graphs, arising from high-order perturbative computations of correlators in planar $\mathcal{N}=4$ super-Yang–Mills, a model closely related to the theory of the strong nuclear force. We benchmark graph neural networks, including graph transformers, achieving robust generalization to larger graphs with up to $99.996\%$ ROC AUC. Then, we analyze how the models can be used to gain a computational speedup compared to the traditional graphical bootstrap algorithm, through shrinking the redundant data by up to $85.5\%$ at the level of denominator graphs. Finally, we study the embeddings of the models to investigate their interpretability.

George Lazarides was a pivotal collaborator and friend to me. We worked together on several projects, developing and exploiting the curvaton hypothesis, which was new at the time. This is a brief overview of our joint research.

It is shown that the co-genesis of baryon asymmetry and dark matter can be achieved through the rotation of a spectator axion-like particle, because of a flip in the vacuum manifold's orientation at the end of inflation. This can occur if the axion has a periodic non-minimal coupling to gravity (while preserving the discrete shift symmetry) in non-oscillating inflation models, where the inflaton field is characterised by a runaway potential. Our rotating axion can generate the baryon asymmetry of the Universe through spontaneous baryogenesis, while at a later epoch it can oscillate as dark matter. We show that in order to avoid fragmentation of the axion condensate during the rotation, we require the non-minimal coupling $\xi\sim(f/m_P)^2$, where $f$ is the axion decay constant.

We propose a nonequilibrium mechanism for Majoron dark energy in which the late-time freezing of a physical Majoron is induced by quantum coherence in a hidden pseudo-Dirac sterile fermion reservoir. The evolving Majoron background derivatively couples to the hidden pseudo-Dirac number current and drives a lagged reservoir response with a finite memory time. In the short-memory regime, the causal response kernel reduces to \(\dot X+\Gamma_{\rm PD}X=\beta\ddot\phi\). The leading linear-response matching \(Q=\alpha X\) then yields an effective scalar equation containing the exchange structure \(q_{\rm exch}\ddot\phi/\dot\phi\). We show that this term can dynamically suppress the Majoron velocity and sustain a response-dominated freezing branch even when the intrinsic Majoron mass is larger than the present Hubble scale. The microscopic origin of the lag variable is identified with the phase-lagged off-diagonal coherence of the hidden pseudo-Dirac ensemble, while the response strength is controlled by a response-weighted hidden density rather than by an independent gravitating component. The resulting state is a metastable nonequilibrium frozen phase with \(w_\phi\simeq -1\), rather than an exactly static cosmological constant.

We study the light-cone quantization of null-strings in $D$ dimensional flat target-space. Incorporating the essential new gauge symmetry and the associated constraint structure of the null-string, allows one to solve for one more degree of freedom (DoF) compared to the standard light-cone gauge, reducing the physical phase space to $(D-3)$ propagating DoF. Quantization is formulated directly in the Schrödinger representation, leading to a Hilbert space of wavefunctions on the reduced configuration space. The space of physical states is built on a reduced phase space associated with the corrected gauge structure. We discuss the ground-state wavefunction and a generic class of excited states. As a direct consequence of the overlooked Carroll-Weyl gauge symmetry of the null-strings, we find the remarkable and perhaps unexpected result that null-strings exhibit a discrete spectrum. Our analysis indicate that there is no critical dimension for null-strings, and $D$ can be arbitrary.

Primordial black holes (PBHs) form when large primordial curvature perturbations re-enter the Hubble radius and exceed the classical collapse threshold. These perturbations originate as quantum fluctuations of the inflationary vacuum, motivating a quantum-information description of the PBH-producing scalar sector. We develop a conservative extension of the standard PBH and scalar-induced gravitational-wave (SIGW) framework in which Gaussian quantum discord is used as a diagnostic of residual quantum correlations, not as a new PBH-formation criterion. We describe each \((\bm k,-\bm k)\) pair as a two-mode Gaussian state and show that, in the pure squeezed limit, discord grows rapidly with the squeezing parameter, so low discord thresholds are automatically satisfied for strongly squeezed modes. The nontrivial regime is the mixed state produced by decoherence. Using a Lindblad open-system description, we motivate a Gaussian loss channel for the scalar covariance matrix and distinguish the discord from a covariance-survival factor \(Q_{\rm dec}(k)\). If the decoherence channel suppresses the scalar two-point covariance, PBH abundance can be affected through the classical collapse variance, while the SIGW spectrum is modified more directly by the factors \(Q_{\rm dec}(ku)Q_{\rm dec}(kv)\) inside the radiation-era convolution. For a narrow scalar peak and slowly varying \(Q_{\rm dec}\), this gives the benchmark scaling \(\Omega_{\rm GW}^{\rm eff}\simeq Q_{\rm dec}^2\Omega_{\rm GW}^{\rm class}\). Thus quantum discord and decoherence provide a controlled way to characterize the quantum-to-classical transition of PBH-producing perturbations, with the clearest imprint appearing in scalar-induced gravitational waves.

These notes are based on six lectures given over three days at the Pre-Strings 2026 school in Shanghai. Day 1 develops neural network essentials, organized around the expressivity, statistics, and dynamics of neural networks, presented with a field-theoretic lens. Day 2 develops a neural network approach to field theory (NN-FT), in which a field theory is defined by a network architecture and a density on its parameters, and surveys recent results. Examples include a universality theorem, a neural network realization of Liouville theory, famous string amplitudes, topological sectors and the Kosterlitz-Thouless transition, Ward identities and anomalies, and a new derivation of the critical dimension of the bosonic string. Day 3 turns the lens around and covers applied AI for string theory: agentic workflows that are changing how the other techniques are implemented, physics-informed neural networks and Calabi-Yau metrics, reinforcement learning and search in the string landscape and in knot theory, and interpretable supervised learning with an eye towards conjecture generation.

We develop a Neural-ODE framework to infer effective bulk metric functions and the charge-weighted gauge potential from boundary fermionic spectra within a static, planar black-hole ansatz. Controlled benchmarks recover the known bulk profiles of the Einstein–Maxwell and Gubser–Rocha models. We then use normalized interaction self-energy targets generated from an extended power-law liquid model with parameters calibrated by angle-resolved photoemission measurements to test the proposed geometric explanation of cuprate strange-metal spectra in a semi-holographic setting. For this application, we use a massless probe in backgrounds with conformal-to-$\mathrm{AdS}_2\times\mathbb{R}^2$ asymptotics and derive a spectral extraction formula from the conserved radial Dirac flux. We identify coordinate/Weyl redundancy and a degeneracy in the scaled Hawking temperature of the normalized inverse problem. The conformal factor remains undetermined, so bulk entropy and the associated contribution to electronic specific heat require independent input. Low-temperature targets are fitted accurately across the studied doping range. In the high-temperature test, however, the present ansatz and optimization search have not yielded a refined geometry that accurately reproduces the thermal spectral shape while preserving frequency symmetry. These results may guide the further development of semi-holographic models for cuprates, and the framework may also find applications in other strongly correlated electron systems.

In this paper, an interactive Holographic Dark Energy (HDE) model is studied in the framework of modified gravity \(f(Q)\). By adopting a power parameterization for the Hubble parameter, the field equations are reconstructed and the evolution of the universe at the background level and tensor perturbations are investigated. Then, using observational data \(H(z)\), the model parameters are constrained and the dynamical behavior of dark energy throughout the history of the universe is analyzed. Also, the study of the evolution of energy density, pressure and the Equation of State (EoS) parameter of dark energy shows that dark energy in the late universe naturally tends to a region close to the cosmological constant behavior, while in the past it followed a distinct dynamical evolution. Stability analysis based on the speed of sound also indicates that the model has good classical stability around the present era. In addition, the compatibility of the current values of the relative density parameters of matter and dark energy with the observational constraints confirms the ability of the model to reproduce the main features of the observed universe. Next, the propagation of gravitational waves in the cosmological context of the model is investigated. The results show that the corrections due to \(f(Q)\) gravity and the interaction between matter and dark energy can affect the evolution of tensor perturbations and produce signatures distinct from the standard scenario. Overall, the findings of this study indicate that the interactive HDE in the gravitational framework \(f(Q)\) can provide a consistent framework for describing the cosmic acceleration and studying the cosmological consequences of gravitational waves.

We study giant graviton-like D3-branes as probe configurations in type IIB supergravity backgrounds AdS$_5\times$SE$_5$, with emphasis on the structure of the five-dimensional Sasaki-Einstein manifolds SE$_5$. These configurations wrap supersymmetric three-cycles in SE$_5$ and rotate at the speed of light along the Reeb direction. We formulate the general problem in terms of the transverse Kähler potential and show that configurations carrying maximal angular momentum can be described by loci where the transverse Kähler potential diverges in suitably chosen coordinates. We quantize a particular set of excitations, similar to those considered in the AdS$_5\times S^5$ case, and show that they are governed by a Fock-Darwin problem with a conical deficit, which generalizes the Landau problem obtained for $S^5$. Succinctly, the information about the geometry of SE$_5$ is encoded in the form of the external potential and the conical deficit. We compute a protected contribution to the superconformal index arising from quantized fluctuations of supersymmetric giant graviton configurations. For the explicit case of AdS$_5\times T^{1,1}$, we recover the finite-$N$ protected index of the dual quiver ${\cal N}=1$ superconformal field theory in the sector captured by a non-Abelian generalization of the quantized degrees of freedom.

Heavy moduli and Kaluza-Klein (KK) gravitons from extra dimensions may evade terrestrial probes but can be produced during inflation, generating primordial non-Gaussianity (NG) through unavoidable couplings to density perturbations. In a warped five-dimensional (5D) model, we compute the full radion- and KK-graviton-mediated bispectra and perform the first search for these signals using Planck 2018 temperature and polarization data. We find no significant evidence for NG, with the maximum significance being $1.8\sigma$ for $m_{\rm KK}\approx 1.6H$. We also identify a 5D setup which naturally generates NG with $f_{\rm NL}\sim 1-50$, within the reach of future surveys.

An observable in an Effective Field Theory (EFT) is an expansion in a set of small parameters, no different than any other perturbation series. Truncating such a series expansion leaves the leading dropped term as the dominant source of error, and that term itself contains a calculable portion. We explore the partial calculation of this next-order error, available at dim-6$^2$ in SMEFT with no additional tools needed to simulate it, and explore how to efficiently use that partial calculation to model the next-order uncertainty in full using a minimal number of nuisance parameters. This estimate of the uncertainty of the EFT signal rate naturally imposes EFT validity by ensuring that bounds are driven by kinematic regions where truncation uncertainties are parametrically smaller than the signal. We incorporate the calculable dim-6$^2$ piece into the signal and cover the remaining higher-dimension uncertainty with a small set of nuisance parameters derived from a scan over Wilson-coefficient values. Our algorithm to determine the relevant nuisance parameters and distributions is automation-friendly and applies to arbitrary truncation choices. We then provide multiple examples of its implementation in high-energy collider processes focused on SMEFT truncated at $\mathcal{O}(\Lambda^{-2})$, where the dim-6$^2$ piece is used to estimate the full $\mathcal O(\Lambda^{-4})$ dependence. In the examples considered here the reduction of nuisance parameters is appreciable, generically reducing the nuisance parameter count by an order of magnitude compared to naïve estimates.

Solvable time-dependent systems provide important settings for studying non-equilibrium physics, where exact results are rare. They are also useful for benchmarking quantum simulations, which can directly probe real-time dynamics beyond the reach of conventional numerical approaches. In this paper, we show that the four-dimensional Chern-Simons theory offers a natural and unifying framework for constructing such systems. Focusing on classically integrable field theories, we consider a generalization of the four-dimensional Chern-Simons theory in which the usual holomorphic one-form is replaced by a more general, spacetime-dependent one-form. This yields a systematic procedure for generating time-dependent integrable field theories and establishes a universal relation: for every theory obtained in this way, the allowed time dependence coincides with the one-loop renormalization group flow. Despite the explicit time dependence, these theories retain Lax integrability and remain solvable by inverse scattering methods. Our construction applies to both ultralocal and non-ultralocal theories and extends previously known time-dependent sigma models to a much broader class of integrable systems. It also admits rewriting as dilaton gravity coupled to matter, producing a large family of classically integrable dilaton gravity theories in two dimensions. We also comment on connections to time-dependent integrable models studied recently in condensed matter physics and non-autonomous integrable systems arising from dimensionally-reduced Einstein gravity.

We use the Poincare parametrization of AdS space to develop a general BRST-BV approach for free fields. A general expression for the BRST-BV Lagrangian of fields with arbitrary masses and symmetry types is obtained. We apply this general framework to study totally symmetric massless, massive, and partially-massless fields with arbitrary integer spin and a continuous-spin field. For these fields, the constrained and unconstrained BRST-BV formulations are developed. We investigate both irreducible and reducible fields. In addition, we demonstrate the matching between the obtained BRST-BV Lagrangian and the metric-like Lagrangian formulated in terms of the modified de Donder derivative. Finally, a realization of AdS space symmetries is obtained within the space of fields and antifields entering the BRST-BV formulation. Modulo the choice of the Poincare parametrization of AdS space, the Lagrangian and the entire approach are manifestly Lorentz invariant.

We investigate the integrability-to-chaos transition and information scrambling in Ising spin networks via a graph-theoretic formulation. Modeling spins as vertices and interactions as edges encoded by adjacency matrices across path, Erdos-Renyi, and Watts-Strogatz topologies, we demonstrate that long-range couplings and heterogeneous degree distributions markedly accelerate quantum information propagation. The Hamiltonian comprises local and normalized non-local interactions; tuning the non-local coupling and field heterogeneity drives integrability breaking. To quantify scrambling, we employ bipartite mutual and tripartite information. Increasing non-local interactions drives tripartite information to large negative values, signaling deep information scrambling. The squared commutators constructed from out-of-time-order correlators (OTOCs) exhibit early-time exponential growth; equivalently, the OTOC four-point functions themselves decay exponentially, yielding quantum Lyapunov exponents that scale systematically with parameters governing the chaotic regime. Complementing this, Krylov complexity reveals rapid operator growth in the chaotic phase, synchronizing with OTOC and mutual information dynamics. Spectrally, the transition manifests as a shift from Poissonian to Wigner-Dyson level spacing statistics. The spectral form factor (SFF) exhibits the characteristic slope-dip-ramp-plateau structure, enabling the extraction of Thouless and Heisenberg times. Crucially, a reduced Thouless time strongly correlates with accelerated information and operator scrambling. Ultimately, this work establishes a unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics, offering insights into thermalization and non-equilibrium dynamics in quantum many-body systems.

We introduce a graph-theoretic framework for representing color-ordered maximally helicity violating (MHV) scattering amplitudes in quantum chromodynamics using coined quantum walks on permutation trees. Each root-to-terminal path corresponds to a distinct color ordering of the external gluons, while local transition amplitudes are assigned according to the spinor-product structure of the Parke–Taylor amplitudes. The walk evolves in coherent superpositions over permutation sectors, giving a dynamical picture of the underlying combinatorics. A quantum-channel formulation based on Kraus operators is also introduced to describe sector-resolved contributions, while a weighted collection operator coherently combines the terminal sectors at a common reference node. A quantum Fourier transform on the coin space is then employed to combine the encoded contributions into the corresponding color-decomposed amplitude. Together, these constructions establish a unified graph-based framework connecting permutation trees, quantum walks, and open quantum systems providing a framework for quantum algorithms to simulate scattering processes in quantum field theory. As an example, numerical results for low-point gluon amplitudes demonstrate that the proposed representation faithfully captures the characteristic Parke–Taylor structure and is consistent with analytical results.

Starting from the gauge invariant action for free string field theory with boundary recently constructed in 2506.05969, we define new gauge invariant observables which are analogous to the Brown-York charges of General Relativity. Just like the Brown-York charges, our observables originate from a boundary tadpole, and are associated to isometries of the SFT gauge group around a given background. The consistency of the construction requires the equation of motion of the background to be satisfied only at the boundary and therefore these observables can also be defined for backgrounds generated by sources in the bulk. As examples of our construction in open string field theory, we compute the flux through the boundary of constant electromagnetic field-strength solutions and the charge associated to the Coulomb solution. As a further example in closed string field theory, we characterize the infinite conserved charges associated to stringy-haired black-hole solutions in two-dimensional string theory. We also construct a generalization of these boundary observables to the full interacting string field theory.

We present a novel approach for solving canonical differential equations for Feynman integrals based on an approximation of the integrals with Chebyshev polynomials. By exploiting the analyticity properties of Feynman integrals, the method constructs rapidly converging polynomial approximations along a path, enabling highly efficient numerical evaluation. Moreover, we introduce an adaptive approximation method that dynamically samples to optimise convergence. We implement this framework in double-precision arithmetic and demonstrate its stability across physical phase space using a series of two-loop, five-point examples. Our proof-of-principle implementation proves competitive with state-of-the-art one-fold integral methods, while requiring little to no case-by-case intervention to handle spurious singularities.

Braiding phenomena, from the charge-flux Aharonov-Bohm effect to anyonic statistics in fractional quantum Hall systems, are paradigmatic manifestations of topology in quantum physics. Ordinary mutual braiding between $p$- and $q$-dimensional excitations occurs in $d=p+q+2$ spatial dimensions. In this work, we introduce a universal construction of mutual statistics in the adjacent dimension $d=p+q+1$, applicable to excitations obeying $\mathbb Z_N$ fusion for arbitrary $N$ and all excitation dimensions $p$ and $q$. The corresponding invariant is the Berry phase accumulated in a simple $4N$-step microscopic unitary process built from local excitation operators on lattices. This process measures the linking of one excitation with the $N$-fold fusion junction of the other, encompassing particle-particle statistics in one dimension, particle-loop statistics in two dimensions, and loop-loop or particle-membrane statistics in three dimensions. We establish the quantization and bilinearity of the invariant and show that its field-theory response is governed by the Bockstein homomorphism, motivating the name Bockstein braiding statistics. Interpreting the excitation operators as open symmetry operators turns the same invariant into a direct microscopic diagnostic of mixed anomalies between symmetries. We demonstrate this diagnostic in a (1+1)D spin chain, where the nontrivial Bockstein braiding phase proves the mixed anomaly between the spin-flip symmetry $\prod X$ and the nearest-neighbor controlled-$Z$ symmetry $\prod CZ$. We construct explicit (2+1)D and (3+1)D lattice analogs, yielding new anomalous symmetry pairs, and apply the framework to strongly coupled (3+1)D continuum gauge theories. Nontrivial Bockstein braiding rules out a fully symmetric gapped phase, obstructs simultaneous condensation of the two excitations, and implies fractionalization of higher-form symmetries.

We formulate an avatar of the Fyodorov-Hiary-Keating conjecture for black hole microstate counts in quantum gravity. By holography, this implies sharp bounds on interval counts of high-dimension primary operators in conformal field theory. The extremal fluctuations of these counts are characterized by a random variable, with a prescribed tail distribution. At large $N$, these order-one erratic fluctuations set a quantitative limit on the resolution of the semiclassical AdS gravitational path integral. Gaussian random models for state counts arise naturally in this context; we express the phenomenon of erratic $N$-dependence in AdS/CFT as a decorrelation property of these models. Our broader point is to suggest that AdS black hole microstate spectra and their field theory duals should exhibit the extreme value statistics of random matrices, lying in the universality class of Gaussian log-correlated fields.

We develop a Floquet–Bloch sideband formulation of the linearized Maxwell–axion system in a coherent periodic axion background. Linearizing around prescribed magnetic and axion fields, we show that the pump generates a sideband ladder of photon and axion branches. Near an isolated folded degeneracy, this ladder reduces to a two-mode crossing whose algebra is fixed by the symplectic signatures of the colliding modes. In temporal fixed-momentum evolution, same-Krein-sign collisions give stable avoided crossings, whereas opposite-sign collisions give parametric instabilities, unifying the axion-photon difference channel with the Mathieu and Masaki-Aoki-Soda resonances. In stationary fixed-frequency transfer, the corresponding flux signatures distinguish bounded forward conversion from forward-backward stop bands and distributed reflection. Ray projection of a temporal pump gives a related but local WKB description of driven forward mixing, with an effective wavenumber distinct from the true axion momentum. External-field diagrams reproduce the sideband selection rules, and full temporal monodromy calculations verify the instability topology and finite-coupling shifts.

We compute some supersymmetric twists of field theories in twistor space, including the minimal supersymmetric and the chiral algebra twists of supersymmetric self-dual Yang-Mills, and the minimal twist of $\mathcal{N}=1$ self-dual supergravity. In the case of $\mathcal{N}=4$ we also find their holographic duals in the framework of chiral holography. We find that the minimal twist of gauge theories in twistor space localizes them to spacetime, making the choice of complex structure manifest, and reproducing the minimal twist on spacetime. For superconformal theories we apply a further twist which localizes the theory to a plane contained on spacetime, reproducing the chiral algebra twist of $\mathcal{N}=4$ sYM. We show that the bulk duals of these twists also localize reproducing the results from twisted holography.

We present a complete classification of integrable Yang-Baxter quantum circuits with open boundary conditions and arbitrary circuit geometries. Starting from the standard transfer-matrix construction with two types of staggered inhomogeneities, we derive a general mapping that determines the arrangement of circuit gates in terms of the inhomogeneities and the system size. We conjecture that time-periodic quantum circuits are integrable whenever the local bulk and boundary gates satisfy the Yang-Baxter equation and the same bulk gate is applied exactly once per period to every nearest-neighbor pair of spins. Our construction also provides an algorithm to detect Yang-Baxter integrability for circuits with arbitrary geometries. Furthermore, we introduce a third type of inhomogeneity, denoted by $\rho$, and demonstrate that the minimum possible circuit depth is four. We show that when these $\rho$-inhomogeneities are placed at the endpoints and in their immediate neighborhood, the resulting boundary gates can be interpreted as single gates acting on multiple sites. Our construction is fully general and applies to regular $R$-matrices, both of difference and non-difference type, together with their associated boundary matrices. As an application, we consider two-qubit gates corresponding to 6- and 8-vertex $R$-matrices of non-difference form satisfying the Yang-Baxter equation, and we construct the associated reflection matrices that generate integrable quantum circuits.