Papers

We analyze the contribution of AdS black hole saddles to the spectral form factor of $d$-dimensional CFTs with a gravity dual. At high temperatures, the analytically continued gravitational action of the large AdS black hole is expected to give a leading large-$N$ approximation to the 'slope' of the spectral form factor. When the CFT is put on a $(d-1)$-dimensional spatial sphere of radius $\ell$, we show that such an evaluation implies unphysical behavior of $Z(\beta +it)$ at large $t\gg \ell$ for $d\equiv5 \,({\rm mod}\; 4)$. A Picard–Lefschetz analysis of a minisuperspace approximation to $Z(\beta+it) $ does reveal the required Stokes phenomena that restore consistency. It is found that for $d>3$, the large AdS black hole saddle loses dominance and subsequently disconnects from the relevant integration cycle at $t=O(\beta)$. For $d=3$, dominance is lost at a time of order $\beta$, while the Stokes disconnection takes place at $t=O(\ell)$. After the large black hole saddle disconnects from the path-integral contour, the slope of the spectral form factor becomes dominated by the low-energy end of the spectrum.

We numerically investigate networks of global $\mathbb{Z}_N$ strings with multi-string junctions in a scalar field model whose vacuum manifold is $\mathrm{PSU}(N)=\mathrm{SU}(N)/\mathbb{Z}_N$. The construction of the model is motivated by the Higgs vacua of mass-deformed $\mathcal{N}=4$ supersymmetric Yang-Mills theory, commonly known as $\mathcal{N}=1^*$ theory, and provides a tractable effective description of string networks with baryon-vertex-like junctions. We perform classical lattice simulations of the formation and evolution of these networks in a radiation-dominated universe. For $N=2,3,4,5,$ and $8$, we find that the networks approach a scaling regime rather than becoming frustrated. The normalization of the string density grows in proportion to the dimension of the adjoint representation, $N^2-1$, while non-minimal-charge components remain subdominant. These results imply that, at least for $N\lesssim 8$, the amplitude of the gravitational-wave energy density generated by the cosmic-string network scales as $\Omega_{\rm GW}\propto \mu^2 (N^2-1)^2$, where $\mu$ is the tension of a unit-charge string.

We develop a bottom-up framework to reconstruct the asymptotic spectrum of light towers in four-dimensional $\mathcal{N}=1$ effective field theories directly from their Kähler potential. Our construction uses the Integral Scaling Relation, which relates the mass scales of towers becoming light at infinite distance to the tensions of EFT strings, together with the Emergent String Conjecture applied recursively upon decompactification. These conditions organize the tower scaling vectors into a lattice generated by the EFT-string vectors and select the globally consistent tower polytopes. When applied to Kähler potentials arising from string compactifications, our algorithm precisely reproduces the known arrangements of towers and duality frames. We then classify the admissible polytopes for asymptotic Kähler potentials $K\sim-\log P(s)$, with $P(s)$ a homogeneous polynomial of degree at most seven, and show that certain apparently consistent Kähler potentials are incompatible with the assumed quantum-gravity constraints. For general polynomials, additional restrictions arise from gluing the tower arrangements across different growth sectors. Remarkably, every tower polytope allowed by our reconstruction can be obtained as a concrete slice of the polytope associated with M-theory on a Joyce $G_2$-manifold. This provides evidence for a form of string universality in which EFT strings act as the fundamental building blocks of the UV tower structure in the EFT perturbative regimes.

Self-dualities and the stacking of symmetry-protected topological (SPT) phases are basic operations on quantum many-body systems. For a $\mathbb{Z}_p$ one-form symmetry in 3+1d these correspond to the Kramers-Wannier-Wegner duality $S$, which is the gauging operation underlying non-invertible duality symmetries, and the stacking of a 1-form symmetry SPT $T$. In the continuum, they form a central extension of $PSL(2,\mathbb{Z}_4)$ for $p=2$, and of $SL(2,\mathbb{Z}_p)$ for odd primes $p$, whose central elements are invertible theories with purely gravitational response. These central extensions are governed by a twisted, graded generalization of the Witt group of abelian anyon theories, which we determine. For $p=2$ the resulting group is the single-qubit Clifford group, with duality and entangler acting as the Hadamard and phase gates. We realize this entire structure microscopically as quantum cellular automata (QCA) acting on a certain local operator algebra associated with a spin lattice Hilbert space on a cubic lattice. Specifically, our local operator algebra is built by starting with all local operators commuting with a $\mathbb{Z}_p$ 1-form symmetry, and taking the quotient by all the (local) 1-form symmetry generators. The central elements can always be extended to the full tensor product algebra with a uniquely defined QCA class. For $p=2$ they are generated by the non-trivial semion QCA, and for odd prime $p$ they are generated by the non-trivial $\mathbb{Z}_p$ Clifford QCA. Consequently the lattice fusion rules reproduce the continuum ones only up to these QCAs and lattice translations, giving rise to fusion rules refined by QCAs.

Quantum cellular automata (QCAs) describe locality-preserving quantum dynamics and connect quantum information, many-body physics, and topological quantum field theory (TQFT). Constructing a QCA from a TQFT, however, is challenging. Although a topological action can produce a commuting Hamiltonian realizing the desired ground state, it does not by itself specify an automorphism of the full local operator algebra. In this work, we develop a unified algebraic construction that extends the commuting generators of the Hamiltonian to a complete separator-flipper algebra on the full tensor-product Hilbert space, providing a microscopic definition of the corresponding QCA. In three spatial dimensions, our formalism unifies all previously known QCA constructions associated with the $\mathbb Z_8\times\mathbb Z_2$ subgroup of the Witt group, including the $U(1)_2$ and $U(1)_4$ QCAs. The same algebraic structure directly yields new infinite families of generalized $U(1)_2$ and $U(1)_4$ non-Clifford QCAs in dimensions $d=4k-1$. We also reformulate the 4-dimensional $w_2w_3$ QCA and use it to develop a general construction of QCAs from TQFTs associated with arbitrary products of Wu classes. This construction includes two infinite families. The first consists of $w_2^nw_3^m$ QCAs in dimension $d=2n+3m-1$, while the second consists of $w_2w_{4k-1}$ QCAs in dimension $d=4k$. As a contrasting result, we explicitly construct finite-depth quantum circuits for the 5-dimensional $w_3^2$ and $w_2^3$ QCAs, thereby proving that they are trivial, in agreement with the cobordism classification. Overall, these results convert invertible TQFTs into microscopic QCAs, provide a scalable route to higher-dimensional constructions beyond the Clifford setting, and open a systematic approach to classifying their stable structures and boundary anomalies.

I argue that dimensional analysis can appropriately be thought of as a gauge theory. This picture naturally leads to the usual quantity calculus through inherent properties of Lie groups, Lie algebras, and representation theory. The gauge theory interpretation is perhaps strongest for non-constant units. I explain how Stevens's classification of scales of measurement can be understood by choices of different gauge groups. Finally, I reinterpret and rephrase the Buckingham-{\Pi} Theorem in a way that also applies to typical gauge theories. Counting the number of ”{\Pi}”s becomes a well-known problem of invariant theory.

We study the strong coupling limit of mass deformed Yang–Mills matrix models, with the aim of understanding when the matrices become effectively commuting. The Yang–Mills interaction classically drives the matrices toward mutually commuting valleys, where the matrices can potentially be interpreted as coordinates of an emergent space. However, taking into consideration the integration measure, commutativity is not automatic since the commuting locus is entropically suppressed, and in the bosonic models with $D\geq3$ the strong coupling limit remains non-commuting. We find that fermions change this competition in a sharp way. As the number of fermionic degrees of freedom is increased, there is a critical value $\mathcal N_c=2(D-2)$, realized by the supersymmetric Yang–Mills matrix models, at which the matrices commute at strong coupling. The same critical models also exhibit universality under deformations by $O(N^2)$, or huge, operators: the normalized eigenvalue densities are insensitive to the microscopic details of the huge operators. Increasing the number of fermions beyond the critical point still gives commuting matrices, but the huge-operator universality is lost. Thus commutativity and universality are related but distinct: the matrix models with supersymmetric field content sit at the critical boundary where we have both.

The coupled ghost and gluon Dyson–Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang–Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

Entanglement entropy at one-dimensional criticality typically follows the Calabrese–Cardy scaling. In the non-Hermitian critical free-fermion systems studied here, however, we find an additional interval-independent contribution $S_{\rm res}=\log(\Delta L)$, which allows the entropy to remain sensitive to energy gaps below the finite-size scale, $\Delta<1/L$. We refer to this term as the residual entropy. To understand its infrared origin, we examine finite-depth non-unitary continuous multiscale entanglement renormalization on a ring. Terminating the critical RG circuit before its singular final layer leaves a two-site infrared state. We calculate the entropy of this state directly from its correlation matrix and recover the same \(\log(\Delta L)\) dependence. The emergent de Sitter geometry provides a complementary geometric interpretation: extremal curves associated with different boundary intervals extend to a common infrared endpoint, suggesting how the entanglement retained there can contribute equally to their entropies.

On two-dimensional manifolds with nonzero constant Ricci curvature, there exists an infinite sequence of scalar fields with nonzero mass parameter that admit a pair of (anti)-holomorphic currents. After suitably defining the theory in de Sitter space ($\mathrm{dS}_2$), correlation functions of these currents obey global conformal Ward identities. We address the question of how this global conformal symmetry manifests as an action on the scalar field. An essential step is in leveraging an equivalent description of the scalar field in terms of a conformal Killing tensor. Through this, we find a conformal symmetry transformation that acts locally on the conformal Killing tensor, but non-locally on the scalar field. We show that the equation of motion transforms covariantly with respect to these conformal transformations, and further find a traceless stress tensor in both $\mathrm{dS}_2$ and $\mathrm{AdS}_2$, locally defined in terms of the conformal Killing tensor, which generates the global conformal isometry transformations.

We investigate the Hilbert space structure for simple theories of gravity with $\Lambda>0$ on closed spatial sections. Our motivation ties to the presence of gravitational saddles in four-dimensional $\Lambda>0$ Einstein-Maxwell theory with $S^2\times \Sigma_h$ topology, where $\Sigma_h$ is a genus-$h$ Riemann surface. Here, as a concrete starting point, the problem is explored for two-dimensional $\Lambda>0$ quantum gravity. We revisit and elaborate on exact results in the matrix model literature. We study gravitational wavefunctions from both the perspective of the Wheeler-DeWitt equation and the gravitational path integral. Though simple, the setting displays many features of general interest such as large volume effects that disrupt the perturbative expansion, topological corrections to the path-integral wavefunction that offend the exact Wheeler-DeWitt equation, and a sphere path integral ${Z}^{(0)}_{\text{grav}}$ with non-trivial structure in $\Lambda$. We discuss candidate inner products for the infinite-dimensional canonical gravitational Hilbert space uncovered by Lian and Zuckerman. By establishing explicit results up to genus-six, we argue that the dominant contribution to the genus-$h$ gravitational disk path integral at large spatial size mimics the behavior of two-dimensional topological gravity. In passing, we show that for ${Z}^{(0)}_{\text{grav}}$ to give rise to a positive counting problem for discretised Riemann surfaces, it must have a negative pre-factor. We contrast our analysis to the more realistic case of timelike Liouville theory.

For $G=SU(N)$ at finite and large $N$, with a totally symmetric representation, we realize the homological block $F_K$ for a knot complement $S^3 \backslash K$, given in the form of the inverted Habiro series, as a half-index of a 3d $\mathcal{N}=2$ theory $T[M_3]$ by studying some examples, which we expect to extend to general knots. From the half-index expression, it is also possible to realize the colored HOMFLY-PT polynomial by taking a certain set of poles. Through the half-index realization, we describe a method for obtaining the $G=SU(N)$ homological block and its $a$-deformed version for $S^3 \backslash K$ from a Habiro series expression for the colored HOMFLY-PT polynomial. We also discuss some properties of partition functions for arbitrary $N$.

We consider the large spin limit $S\to\infty$ of the OPE coefficient for two maximal giant gravitons and a spinning operator with finite twist in planar $\mathcal{N}=4$ super-Yang-Mills theory. Up to an overall normalization factor, this OPE coefficient exhibits a power-law scaling of the form $S^{d(g)}$. We provide strong evidence that the exponent $d(g)$ is free from finite size corrections. Consequently, the all-loop asymptotic expression for the OPE coefficient can be used to determine $d(g)$ exactly. We develop a systematic method to compute the scaling function $d(g)$ for arbitrary values of the 't Hooft coupling $g$. At weak coupling, our result agrees perfectly with the available field-theoretic results up to three-loop order. At strong coupling, we present the first three orders as concrete predictions. We further provide the finite-coupling result and show that it interpolates smoothly between the weak- and strong-coupling regimes.

We propose a relational bundle-geometric formulation of the gravitational path integral by invoking the new tool of quantum reference frames (QRFs), which in gravity are gauge-covariant coordinate systems constructed from the available field content. Formulated in terms of relational (frame-dressed) observables, this yields a manifestly gauge-invariant path integral without ghosts and anomalies, and in which observables and their correlators are local to a frame. While eliminating the need for gauge fixing, it is equivalent to Faddeev-Popov versions in which the QRF is gauge-fixed, recovering certain previous proposals. A key feature is its covariance under QRF changes: it is a perspective-neutral path integral which encodes all internal QRF perspectives and the transformations between them. This leads to several qualitative predictions: local correlators and time evolution of relational observables in one QRF perspective become fuzzy in another, and a new spectrum of relational vacua arises. Comprised of frame-dependent no-boundary and asymptotic ground states, a vacuum from one perspective appears generally excited in another. Finally, we construct gauge-invariant, yet frame-dependent effective actions by coupling sources exclusively to relational observables, setting the stage for a relational definition of renormalization.

Stochastic quantization defines a Euclidean quantum field theory as the equilibrium of a fictitious-time Langevin dynamics, which reaches the Gibbs measure asymptotically. We show that this quantization can be formulated as a finite-time stochastic optimal control problem. A tractable reference process, naturally supplied by the free theory when available, provides an Ornstein–Uhlenbeck dynamics, while the full interaction enters as a reference-corrected terminal cost. The optimal control is a Doob-transform force that steers the path-reweighted terminal ensemble to the target at a prescribed time and for a given noise amplitude. A neural network learns the residual control, realizing this optimal stochastic quantization (OSQ). Because the path weights are exact, imperfect training increases the variance of estimators but does not introduce model bias. On multimodal potentials we recover all modes at finite time and find that the noise amplitude sets a practical diffusion-horizon window. In two-dimensional lattice scalar $\phi^4$ theory we recover observables from hybrid Monte Carlo simulations near the critical point. Quantization is thereby formulated as control rather than equilibration.

Multi-winding Wilson loops (“Wilson spools”) in 2+1-dimensional gravity can reproduce one-loop partition functions of local free fields in the bulk. Bulk free fields have a second-quantized Fock space, and the AdS/CFT correspondence suggests that the associated multi-particle sectors are dual to multi-trace primaries in the CFT. In this note, we use standard symmetric-function methods to show that the Wilson spool in thermal AdS$_3$ can be recast as a sum over $single$-winding Wilson loops — one for each multi-trace primary. In a companion paper to appear, we will view Wilson networks and TQFTs as the natural language of non-perturbative bulk quantum gravity. The present note illustrates how this can apply to $local$ bulk fields, and not just defects: a bulk (generalized free) field is to be viewed as a full tower of multi-trace Wilson lines. We further show that the $SL(2)$ descendants of each multi-trace primary, together with the boundary gravitons of the AdS$_3$ background, correctly reproduce the full Virasoro character of each module. In this language, the role of a light insertion on a heavy primary is played by a topological Verlinde line. This allows us to obtain a “microscopic" description of one-loop determinants on the smooth BTZ handlebody. A spatially wound probe Wilson line on a torus with a contractible $thermal$ cycle can be traded for a Verlinde line inserted on a dense family of heavy Polyakov loops — with the roles of the two cycles exchanged, so that the $spatial$ cycle is now contractible. The vacuum row of the modular $S$-kernel acts as the (approximate) density of the heavy primaries. This reinforces the case made in arXiv:2601.18775 that a smooth horizon is a stand-in for an ensemble of quantum states, each produced by a heavy Wilson line that appears as a singular horizon in the semi-classical limit.

We develop a systematic analytic method for studying high-order pole-skipping in near-extremal holographic black holes. In the near-extremal regime, approaching the limit $T\to0$, the near-horizon geometry develops an approximately $\mathrm{AdS}_2 \times \mathbb{R}^{d-1}$ structure; we show that the mode index $q$ labeling pole-skipping points is identified with the IR conformal dimension $\Delta_{\mathrm{IR}} = q$ in the emergent $\mathrm{AdS}_2/\mathrm{CFT}_1$ correspondence, providing a concrete physical interpretation of the subleading pole-skipping tower. The method reorganizes the near-horizon Frobenius expansion according to powers of temperature. This reveals a temperature-graded hierarchical structure that reduces the $n$-th-order pole-skipping condition to a factorized algebraic equation:each pole-skipping momentum depends only on the mode index $q$, not on the order $n$. This $n$-independence produces a high degeneracy as $T\to 0$, where pole-skipping momenta at all orders collapse onto a discrete set of values determined by near-horizon geometry and the scalar field mass; these values can be expressed in terms of thermodynamic quantities such as entropy density and specific heat. In the limit $n \gg 1$ (with $nT$ remaining small), the leading pole-skipping momenta grow asymptotically as $k_{n,n} \propto n$. We compute leading temperature corrections and verify our predictions through numerical analysis of the Dyonic Gubser–Rocha model. The results confirm that high-order pole-skipping at low temperature is governed by near-horizon physics. This provides analytic access to pole-skipping points well beyond those accessible by standard determinant methods and clarifies the structure of holographic Green's functions in the low-temperature regime.

We study the production of ultra-high-energy particles via the Bañados–Silk–West (BSW) mechanism in the pre-merger phase of binary systems detected by LIGO-Virgo-KAGRA. By solving the geodesic equations for charged particles in magnetized Kerr spacetime with fields of $B \sim 10^{12}$–$10^{14}$~G, we demonstrate that collisions near the horizon can achieve center-of-mass energies $E_{\mathrm{cm}} \sim 10^{18}$– $10^{20}$~eV, placing them firmly in the ultra-high-energy cosmic-ray (UHECR) range. We systematically explore the parameter space of merger remnants, varying black hole mass ($M \sim 20$–$150\,M_\odot$, characteristic of the binary black hole population), dimensionless spin ($\chi_f \sim 0.7$–$0.9$), magnetic field strength, and particle angular momenta. Our analysis reveals three distinct acceleration regimes: a gravity-dominated regime ($B < 10^{12}$~G) with negligible magnetic enhancement; a transition regime ($10^{12}~\text{G} \lesssim B \lesssim 10^{13}~\text{G}$) where gravitational and magnetic effects compete; and a magnetic-dominated regime ($B > 10^{13}$~G) where fields amplify collision energies by nearly an order of magnitude. For the 34 gravitational-wave events with high remnant spins ($\chi_f > 0.7$), we compute the maximum achievable energies, finding that systems with $\chi_f \gtrsim 0.85$ and $M \gtrsim 100\,M_\odot$ can reach $E_{\mathrm{max}} \sim 10^{20}$~eV. Our results establish magnetized binary mergers, particularly black hole–neutron star systems and postmerger black hole remnants formed in binary neutron star coalescences, as promising sources of UHECRs and provide quantitative predictions linking gravitational-wave observables to particle acceleration efficiency.

We describe a bounded search for local and global anomaly-free six-dimensional $(1,0)$ models with tensor number $T=1$ and gauge group containing a diagonal abelian factor $U(1)_{R+}$. The abelian factor is the diagonal combination of the usual gauged $U(1)_R$ and a $U(1)\subset Sp(n_H)$ acting on hypermultiplets. We have searched for locally and globally anomaly-free $G_1\times U(1)_{R+}$ and $G_1\times G_2\times U(1)_{R+}$ models, subject to restrictions on the ranks of the simple factors and on the maximal charges carried by matter. We find that, unlike the case of $U(1)_R$ gauged models which are relatively rare, the diagonally gauged ones offer a rich landscape. We also study the 6D vacua of these models and find that they admit supersymmetric 6D Minkowski vacua, for which the diagonal nature of the R-symmetry gauging is necessary.

We study the defect contribution to the entanglement entropy of a spherical region centred on four-dimensional superconformal RG interfaces. These interfaces are supersymmetric codimension one defects separating the Leigh–Strassler SCFT vacuum and the $\mathcal{N}=4$ SYM theory deformed by spatially varying mass terms. Exploiting the holographic dual to these interfaces, we extract a cutoff-independent interface contribution to the entanglement entropy, $\mathcal{C}^I$. We quantify the non-trivial dependence of $\mathcal{C}^I$ on the supersymmetric mass deformation, and observe a scaling regime for large deformations. We further relate $\mathcal{C}^I$ to the renormalized on-shell action and the stress-tensor one-point function of the interface theory. Our results provide the first fully backreacted holographic computation of this entanglement quantity for superconformal RG interfaces in more than two dimensions.

We construct a covariant representation of the causal logic for the Dirac system and the electron, based on the conserved Dirac probability current and a general current-to-localization procedure for achronal regions. A polynomial decay estimate, derived by a non-stationary phase argument, verifies the conditions required to define covariant achronal localization for the full Dirac system. Extending this localization to complete spacetime regions yields the corresponding causal-logic representation; restriction to the positive-energy invariant subspace gives the analogous construction for the electron. We establish several structural properties. On Euclidean space, Dirac localization agrees with canonical projection-valued localization, while its position operator differs from the Newton–Wigner operator by an explicitly determined bounded self-adjoint correction. Full Dirac achronal localization is projection valued and represents achronal separateness by orthogonality, thus satisfying microscopic causality. After compression to the electron subspace, it becomes positive-operator valued while preserving causality. We further extend known results from spatial to general achronal regions, prove separation and norm-one criteria, and analyze the high-boost limit, obtaining Lorentz contraction in a precise probabilistic sense. Finally, we discuss the electron–positron decomposition and the state transformation induced by position measurements, showing that measurement-induced positron production is universal and independent of the specific measuring device.

The standard "no-go theorem" against late-time solutions to the Hubble tension is essentially a normalization wall, since Baryon Acoustic Oscillation (BAO) measurements constrain the product $H_0r_d$, with $r_d$ the sound horizon at baryon drag. However, late-time solutions (which keep $r_d$ fixed) are tightly constrained not only by the BAO normalization $H_0r_d$, but also by the shape of the expansion history, i.e. the dimensionless expansion rate $E(z) \equiv H(z)/H_0$. We show that, if $r_d$ and the acoustic angular scale $\theta_s$ are fixed, an increase in $H_0$ needs to be matched by an equal fractional increase in the dimensionless distance integral $I \equiv \int dz/E(z)$: $\delta H_0/H_0 \simeq \delta I/I$. We use this to quantify the "shape wall" set by relative distance constraints on $E(z)$, which we reconstruct nonparametrically, using Gaussian Processes and the latest unanchored Type Ia Supernovae (SNeIa) and BAO data. In our most conservative analysis using PantheonPlus SNeIa and DESI DR2 BAO data, we find a maximum fractional increase in $H_0$ of $\lesssim 2\%$, falling well short of the $\gtrsim 8\%$ required to solve the tension. This shape wall holds even in the presence of early-time new physics, and limits the maximum increase in $H_0$ which can be contributed by late-time modifications to $E(z)$ at fixed $\theta_s$. Therefore, late-time modifications, whether invoked alone or alongside early-time new physics, face not only the well-known normalization wall, but also a stringent percent-level shape wall.

The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.

We investigate how the particle spin modulates chaos bound violations in Lorentz-violating black hole spacetimes within the framework of Bumblebee gravity. Using the Mathisson-Papapetrou-Dixon formalism, we analyze the effects of spin-curvature coupling, Lorentz symmetry breaking, and the cosmological constant on the orbital instability in static spherically symmetric (A)dS black holes. We find that the particle spin provides a tunable mechanism for the violations by lowering the critical angular momentum required to enter the violation regime. The Lorentz-violating parameter suppresses the violations by reducing the accessible parameter space and the critical charge. Meanwhile, a negative cosmological constant decreases the violation region but enhances the violation magnitude for allowed configurations. Our results demonstrate that the spin and Lorentz symmetry breaking jointly regulate the interplay between orbital instability and black hole horizon properties.

We study energy-energy correlators (EEC) in planar $\mathcal{N}=4$ super Yang-Mills theory at strong 't Hooft coupling $\lambda$. We consider the EEC in states created by half-BPS operators of arbitrary dimension $p$, and determine the corresponding event-shape function up to order $\lambda^{-3/2}$ from the worldsheet representation of the AdS Virasoro-Shapiro amplitude with Kaluza-Klein external states. For $p=2$ we compute the second curvature correction, which completes the EEC through order $\lambda^{-2}$; the new contribution improves the agreement with recently derived non-perturbative bounds at intermediate coupling. We further develop a complementary method in which the strong-coupling expansion coefficients of the EEC are extracted directly from the Wilson coefficients of low-energy expansion of the AdS Virasoro-Shapiro amplitude, and find the two approaches in perfect agreement.

Electric and magnetic Carrollian actions for fermions of arbitrary spin in any spacetime dimension are defined as inequivalent $c \to 0$ limits of the relativistic Fang-Fronsdal actions.

In this article, we have calculated the time-dependent thermal one-point function of massive operators within an expanding universe. We employ the Randall-Sundrum II braneworld model combined with a $p$-brane gas in the bulk, enabling us to represent various matter-dominated cosmological scenarios localised on the brane. Applying the geodesic formula introduced by Grinberg and Maldacena in \cite{Grinberg:2020fdj}, we have calculated the thermal one-point functions of massive operators within the universe. The time-dependent one-point functions for different matter-dominated universes, both single-component and multi-component, are derived from the brane's evolving radial position. The time-dependent positions of the branes have been obtained using the second Israel junction condition. Additionally, we have analyzed the early and late-time behaviors of the thermal one-point function across various matter-dominated universes.

We expand the Einstein–Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge–Wheeler gauge of the Gaddam–Groenenboom–'t~Hooft near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a vanishing theorem: at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero. This is a framework-specific statement: even RW gauge, GGV sector, leading soft order. The surviving interaction lives in the trace sector; its on-shell equal-$\ell$ weight $W(\lambda,\lambda,\lambda)=-3\lambda(2\lambda^2+\lambda+3)/(\lambda+1)^2$, follows from two independent derivations agreeing to machine precision. We simulate the resulting Hamiltonian at two complementary scales. On IBM Qiskit/Aer, with exact cross-checks, the hardware-format circuits confirm quantitatively what two structural facts already predict, a conserved charge that only the cubic vertex violates (opening $\phi\phi\to hh\to4\phi$) and a resonance-free boost spectrum (gap $\to1/2$): the longitudinal channel is perturbatively rigid, and the simulation measures the residual dressing ($d_{\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar). A symmetry-graded matrix-product-state evolution then climbs the multipole ladder to sixty modes, the $120$-qubit register, and settles the one question the multiplet cannot: on a late-time measure common to both engines the inelasticity converges to $\bar\eta_\infty\simeq0.16$ (understated by the single multiplet), the dressing stays area-law with peak entanglement $\simeq0.45$ nats far below the Page value, and the result is cutoff-converged and robust to $96$ qubits at larger occupation. The rigidity therefore persists rather than scrambling as the register grows.

In soliton theory, both the gauge-theoretical method and the Bäcklund transformation yield soliton equations from the compatibility condition of a pair of linear equations. Therefore, it is necessary to clarify the similarities and differences between these two methods. The Bäcklund transformation defines a transformation from one soliton solution to another. In particular, restricting the transformation to solutions with different soliton numbers yields interesting insights. Using several examples, we demonstrate how soliton solutions with different soliton numbers are constructed.

A rigorous statistical analysis of Regge-type trajectories for light non-strange meson mass spectra is carried out, which explicitly accounts for experimental uncertainties. We test three scenarios: a linear model with distinct radial ($n$) and orbital ($l$) slopes (Model 1), a linear model with a universal slope (Model 2), and a nonlinear model featuring a universal slope and a Dirac-Coulomb-type term $\propto (l+1)^{-1}$ (Model 3). Optimization is performed using a nonlinear $\chi^2$ minimization framework, where the intrinsic theoretical model uncertainty is determined self-consistently by enforcing $\chi^2/\text{dof} = 1$. To ensure robust model selection, we employ the Akaike and Bayesian information criteria alongside complementary statistical tests. Our analysis demonstrates that moderate deviations from linearity in the Regge spectrum are predominantly localized within the $S$-wave resonance sector. These distortions are successfully accommodated by the nonlinear correction in Model 3, from which an approximate Coulomb-type degeneracy, $m^2(n,l) \propto n+l$, emerges as a statistically robust feature. Furthermore, we show that the $l$-dependent correction to the principal quantum number in light non-strange mesons is consistent with the leading-order relativistic correction to the Coulomb problem.