Papers

Working in the Worldline Quantum Field Theory framework, we obtain the classical gravitational Compton amplitude through the fifth post-Minkowskian order, $\mathcal{O}(G^5)$. At this order, the point-particle description must be supplemented by the leading static tidal operators. After removing lower-order iterations, we extract the corresponding $N$-matrix element and match it to black-hole perturbation theory. The matching fixes the static tidal Wilson coefficients to zero, providing confirmation of the vanishing static Love numbers of a Schwarzschild black hole.

Head movements require integration of visual, proprioceptive, vestibular, and cervical motor signals. The dynamical principles governing their temporal organization remain unclear. We tested whether a Pais-Uhlenbeck oscillator – a higher-derivative model with one internal frequency parameter $\omega$ – can model head kinematics during virtual-reality-based head pointing. Our model predicts a parabolic relationship between movement duration ($T$) and smoothness (log-dimensionless jerk, $LDLJ$) that we have experimentally checked. Sixty-two healthy young adults performed horizontal and vertical head movements with an amplitude of 30{\deg}. Movement duration, endpoint accuracy, peak angular velocity, overshoot, and $LDLJ$ were extracted from headset kinematics. A mixed-effects parabolic regression confirmed the predicted $LDLJ$ vs $T$ parabolic relation ($R^2 = 0.851$). The quadratic coefficient was not significantly modified by direction or participant, but the intercept and linear coefficient differed between horizontal and vertical movements. As an internal consistency check of the model, we find that the parameter $\omega$, as estimated from the regressions, gives time durations that closely match the measured ones. These findings outline a nonlinear temporal organization of head pointing modulated by direction-specific biomechanical constraints, and suggest that higher-derivative mechanics may provide a principled, non-invasive framework for quantifying cervical motor planning, warranting further validation in clinical populations.

We present a reformulation of four-dimensional chiral gravity in terms of a chiral gauge connection and a Clifford-valued coframe. The exterior algebra generated by $e^a \gamma_a$, together with the gauge curvature $F$, provides a natural and systematic construction of gauge-covariant differential forms. We show that suitable combinations of the chiral actions reproduce Einstein–Cartan–Holst gravity with a cosmological term. The original superconnection invariants yield only algebraic fermionic equations, so the fermionic one-forms do not propagate but instead generate a mass-like mixing between the two chiralities. Spinor propagation is supplied by a spinorial BF-type term, which under the matter ansatz reduces to the standard first-order Weyl kinetic action, including the torsion coupling. We also review the symmetry and variational properties of the matter ansatz, including its Lorentz equivariance, its relation to residual supersymmetry and twistor spinors, and the connection between the reduced and unrestricted field equations.

Within the subregion complexity-volume conjecture, we numerically compare holographic subregion complexity (HSC) and holographic entanglement entropy (HEE) for a strip in unbalanced Stückelberg holographic superconductors. Varying the Stückelberg parameter $\gamma$ yields both second- and first-order transitions. Both observables signal these transitions, but with markedly different robustness. The qualitative HEE signatures persist across strip widths, and the finite part of HEE remains smaller in the superconducting phase than in the normal phase. The HSC is instead strongly width dependent: its temperature trend is opposite to that of HEE at small $\ell$ and agrees with it at large $\ell$. Consequently, the superconducting and normal HSC branches reverse their relative ordering, creating a crossover region where they nearly coincide. There, HSC alone cannot reliably determine the occurrence or order of the transition, and the physical branch must be selected from the grand potential. Thus, HEE provides a more robust diagnostic, whereas HSC is a scale-dependent probe whose interpretation depends explicitly on the subsystem size.

We derive a compact analytic formula for the one-loop triangle correlator of conformally coupled scalars in de Sitter space. The result is organised as six leading-singularity prefactors multiplying pure weight-two functions of the six energy variables. It contains forty-two dilogarithms, compared with approximately one hundred and twenty in the previously known closed-form representation, and requires no auxiliary regulator. The dilogarithms occur in Galois-conjugate pairs, making each contribution separately real throughout the physical region. We validate the result numerically. Moreover, we show that its symbol can be derived directly from the dressed integral representation or, independently, bootstrapped from Landau singularities and general consistency conditions. Finally, we show that the correlator (in a suitable normalization) is a Stieltjes function of each squared energy separately and is jointly completely monotone in all six squared energies. These structures suggest a route towards higher-point one-loop cosmological correlators.

We study the existence of Einstein scales and compatible metrics in Grassmannian geometry. As a special case, this includes the conformal-to-Einstein problem for anti-self-dual (ASD) conformal structures. In the ASD setting, given a genericity condition algebraic in the Weyl curvature, we obtain necessary and sufficient conditions for the existence of a local Einstein scale that refine those previously appearing in the literature. We also prove that in Riemannian signature, a non-Ricci-flat ASD-Kähler metric is locally conformally Einstein if and only if it has a holomorphic Killing vector field with anti-self-dual derivative proportional to the Ricci spinor. Next, we consider some generalisations of the ASD conformal-to-Einstein problem for $(2n,2)$-Grassmannian structures. When $n > 1$, given an analogous genericity condition, we obtain necessary and sufficient conditions for the existence of a local Einstein scale. Using tractor calculus, we obtain algebraic obstructions to the existence of compatible metrics and show that the unique submaximally symmetric model of the geometry has the submaximal number of linearly independent compatible metrics.

We show that the Coulomb branches of 5d $\mathcal{N}=1$ necklace quiver gauge theories on $\mathbb{R}^3 \times T^2$ are identified with the phase spaces of elliptic spin Ruijsenaars-Schneider models with dynamical inhomogeneities. This identification resolves the long-standing problem of determining a Poisson structure and a quantization of these models. We further show that the resulting quantum system is the integrable system governing supersymmetric indices of 4d $\mathcal{N}=1$ theories of class $\mathcal{S}_k$.

We formulate a non-Abelian theory of network compatibility in which dynamical transformations reside on the links. Gauge covariance follows from the freedom to choose local representation frames, while plaquette holonomies quantify the incompatibility of closed-loop transformations. For an SU(2) model on the complete simplicial 2-complex with quenched random plaquette couplings, parallel-tempering simulations reveal a continuous disorder-driven phase transition characterized by the network compatibility $M_P$. As the disorder strength approaches the critical value, the compatibility drops rapidly to a value that decreases with system size, while the frustration energy of the network sharply rises. Moreover, analysis of connected replica-overlap width provides no evidence for thermodynamic replica-symmetry breaking. Instead, the high-disorder regime sustains a nearly constant integrated adjacent correlation as the system size increases. Therefore, rather than a frozen gauge glass or a featureless disordered “gas” phase, dense topological frustration produces a non-glassy correlated gauge liquid in which individual pair correlations are geometrically diluted while a finite integrated correlation survives.

We compute the renormalized scalar vacuum polarization $\langle \phi^2 \rangle$ of a massive, non-minimally coupled quantum field in the Hartle–Hawking state exterior to a family of static, spherically symmetric quantum-corrected, effective and regular black holes: the Kazakov–Solodukhin quantum-deformed black hole, the two effective loop-quantum-gravity geometries of Zhang–Lewandowski–Ma–Yang, the renormalization-group improved Schwarzschild black hole of Bonanno–Reuter, and the Bardeen regular black hole. We adapt the extended point-splitting mode-sum formalism, implemented as a high-performance code, and present the exterior profile of the vacuum polarization over a grid of the quantum-deformation parameter, the field mass $\mu=mM$ and the curvature coupling $\xi$. The five geometries display qualitatively distinct horizon responses. In all five geometries the deformation imprint is governed by the sign of the background Ricci scalar through the DeWitt–Schwinger curvature term linear in $(\xi-1/6)\mathcal{R}$, and is strongly suppressed at conformal coupling. We verify this both in magnitude and in the $\xi$-dependence. In the near-extremal regime of the two geometries with inner horizons we find a sign change of the horizon polarization at light field mass – absent for Reissner–Nordström at matched temperature and removed by conformal coupling – identifying a genuinely quantum-geometric, de-Sitter-core-driven regime. Every result reduces to the Schwarzschild value in the classical limit, validating the calculation.

We investigate the axial Ward identity for massive fermions under a constant magnetic field at arbitrary strength, maintaining an arbitrary spacetime configuration of a perturbative electric field. We show that a spatially modulated electric field prevents the exact cancellation between the anomaly and pseudoscalar terms, generating a local axial-charge source even in the adiabatic regime where the frequency is subthreshold to massive-fermion production. Remarkably, unlike conventional magnetic responses, this charge generation is dominated not by the contribution of the lowest Landau level, but by those of the higher Landau levels. Our findings provide a microscopic foundation for anomaly-induced transport and anomalous optical responses in gapped systems. In particular, we find that the spatially modulated chiral magnetic effect in weakly gapped Weyl semimetals that exhibits a linear suppression of the magneto-resistance by the magnetic-field strength instead of the renowned quadratic suppression.

Recently, a set of coupled singlet-octet universal Lindblad equations (ULEs) was derived within the framework of non-relativistic QCD (NRQCD) to describe quarkonium dynamics in the quark-gluon plasma (QGP). These equations provide a unified quantum description spanning the quantum Brownian and quantum optical regimes. In this work, we further develop this framework and establish its connection with semiclassical transport. We first derive the universal Lindblad equations within the potential non-relativistic QCD (pNRQCD) effective field theory and show that they coincide with the small-dipole limit of the NRQCD ULEs. We then derive the semiclassical limit of the NRQCD ULEs, obtaining a set of coupled singlet-octet Boltzmann equations. To our knowledge, this is the first derivation of Boltzmann transport equations directly from the universal Lindblad framework. The resulting equations are valid beyond the small-dipole approximation, allowing the evolution of heavy-quark pairs from compact to widely separated configurations. Taking their small-dipole limit allows a direct comparison with the Boltzmann equations of Yao et al. [Phys. Rev. D 99, 096028 (2019)], which were derived within pNRQCD from the Davies secular equation, relying on the rotating-wave approximation (RWA). While the singlet equations are found to be in near-complete agreement, the octet equation contains an additional collision term describing transitions within the continuum of octet scattering states, which is absent from the RWA-based derivation. Finally, we derive the leading quantum correction to the singlet Boltzmann equation. Our results establish a more general and systematic theoretical foundation for the semiclassical transport description of quarkonium in the QGP.

Ostrogradsky's theorem shows that higher-derivative dynamical systems inevitably yields a Hamiltonian featuring a ghost mode that is unbounded from below. However, we argue that this theorem is inapplicable to gravitational systems, as the Hamiltonian constraint, which encodes background independence by dictating that the total Hamiltonian vanishes, holds strictly. The ghost mode obeying this constraint constitutes an indispensable component in the construction of space and time. Nevertheless, it should be underscored that the use of the weak-field (graviton) approximation, being a background-dependent scheme presupposing the existence of absolute time, invokes this theorem; consequently, it is allowed only in the domain below the Planck scale, where second derivative terms dominate.

The fluctuations in the phonon vacuum state can lead to zero point density fluctuations in a material, which in turn lead to local zero point fluctuations of the dielectric properties of the material. We argue that the density fluctuations lead to a fluctuating force on a test charge, such as an electron, located a short distance outside of the material. This force is due to fluctuating dipole moments inside the material, and produces Brownian motion of the electron. We calculate the mean squared velocity of the electron in both the normal and transverse direction relative to the boundary of the material. The result is nonzero in both directions, but larger in the normal case. We estimate the magnitude of this quantum Brownian motion and find that, in some cases, it can exceed the effects of both thermal motion and quantum momentum uncertainty. This suggests that the effect may be observable, and could constitute a source of quantum noise in nanoscale devices. It also potentially offers a means to remotely sense zero point density fluctuations in a material.

Radiative corrections at the percent level can shift the predictions of $\alpha$-attractor and Starobinsky-like models into the region of the $(n_s,r)$ plane preferred by ACT DR6. We show that the decisive property is not the size of a correction but whether it is removable. In the slow-roll $N$-formalism the observables are functionals of $\eps(N)$, and equality of $\eps(N)$ on an interval reconstructs the potential up to an amplitude rescaling and a shift of the canonical field. A larger class, selected by $(V/V')\Delta'={\rm const}$, preserves the leading predictions and provides a criterion for any proposed deformation. In weakly nonlocal completions of $R+R^{2}$ the improvement scale $\mu=H(\phi)$ makes the renormalization-group time one half of the logarithm of the tree potential, so the local one-loop flow passes the test and evolves the model onto the E-model family $V\propto(1-e^{-\sqrt{2/3}\,\phi/\mpl})^{p}$ with $p=2+K$. Since the divergent local beta functions of these super-renormalizable completions are one-loop exact, no higher-loop local running modifies this picture. The induced shifts are $\ord(\ln N/N^{2})$ in $n_s$, obtained in closed form for the removable part and numerically for the rest. The number of $e$-folds, which the criterion does not protect, contributes at the \red{$22\%$} level with an opposite sign. Matter-induced corrections fail the same test at leading order, which is why they shift the predictions. Among the deformations proposed since ACT DR6, an $R^{n}$ term in $f(R)$ gives $(V/V')\Delta'=\ord(N^{n-1})$, so only $n=2$ is removable, and no deformation that increases $n_s$ satisfies the criterion. For Standard Model matter, the removable channel is fixed by the Higgs nonminimal coupling alone and is $\ord(10^{-11})$, because the measured amplitude sets the coefficient of $R^{2}$ to $5.1\times10^{8}$.

We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor $z$ characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters $\alpha$ and $\beta$ and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for $\alpha \beta =1$, whereas for $\alpha \beta \neq 1$ parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate weak radiative tails and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.

We consider the $d\geq 4$ non-polynomial pure gravity theories defined so that their 2D reduction to spherical symmetry minimally modifies that of General Relativity at small distances. They satisfy Birkhoff theorem and admit exact black hole solutions for an arbitrary number of couplings. These solutions have a logarithmic leading correction to the entropy and a quantum-like correction to the Newtonian potential, both arising from the regularised critical order $d=2p$ theory, which is related in even dimensions to the Euler characteristic of the 2D orbit space. These black holes can be made regular, without the need for infinite towers of corrections, using invariants of any order $p>d/2$. In even dimensions, their smoothness is linear in the number of corrections and does not require fine-tuning. We construct a class of theories admitting as unique (massless) vacuum an extremal black hole deformation of (A)dS$_4$ or M$_4$ with vanishing entropy, so that Nernst's third law of thermodynamics is satisfied without discontinuity in the entropy. We show that a Maxwell field does not disrupt the regularity of the metric, and that simple non-minimal couplings in the action enable to regularise the electric field. Considering infinite towers of corrections, we construct quasi-regular black holes with one horizon as well as regular (A)dS-core ones with a near-extremal inner horizon for any mass. When charged, these two types of black holes prevent or tame the mass inflation provided the mass and charge satisfy an inequality of the form $M > \alpha \ell + \beta Q^2 / \ell$, where $\alpha$ and $\beta$ are numerical factors depending on the specific model, while $\ell$ is the length scale controlling the high-energy corrections. The quasi-regular black holes are sufficient to resolve the Coulomb singularity without the need for non-minimal couplings.

The nature of the $X(3872)$ exotic hadron remains one of the most debated questions in hadron spectroscopy. We calculate its magnetic moment within a non-relativistic quark model that includes the three-body force arising from the cubic Casimir operator of $SU(3)_C$ with consistent dimensional analysis. Unlike previous works that used an uncontrolled large coupling, we fix the three-body strength using the realistic value of $\sim 10$–$20$ MeV extracted from the recent analysis of Noh et al.~(2024) based on lattice QCD and baryon spectroscopy. We find that the magnetic moment predictions fall into two distinct regions: the pure color-singlet configuration yields $\mu_X = -0.99 \pm 0.02\,\mu_N$, while the compact configurations yield $\mu_X = -1.17$ to $-1.23\,\mu_N$. The difference between the two compact scenarios ($0.06\,\mu_N$) is comparable to the systematic uncertainty of the model ($\sim 0.15\,\mu_N$) and should be interpreted with caution. However, the distinction between the pure color-singlet and the compact scenarios ($\sim 0.18$–$0.24\,\mu_N$) is larger than the estimated model systematic uncertainty and may provide a qualitative structural indicator. We emphasize that the pure color-singlet configuration is a simplified proxy for a molecule and does not represent a physical $D^0\bar{D}^{*0}$ molecule with large spatial extent. A full molecular treatment would require coupled-channel dynamics and long-range pion-exchange potentials, which are beyond the scope of this work. We also resolve a long-standing dimensional inconsistency in the cubic Casimir three-body force formulation and demonstrate through a detailed sensitivity and uncertainty analysis that our conclusions are robust for the physically relevant range of the three-body coupling.

We consider a conformally coupled scalar field in four-dimensional global anti-de Sitter space with Robin boundary conditions, parametrized by an angle $\alpha$. On the boundary cylinder $\mathbb{R}\times S^{2}$ these conditions realize the double-trace deformation $\tfrac12\lambda\!\int O^{2}$ of the dimension-one operator $O$ in the alternate quantization with $\lambda=\cot\alpha/L$. Because the conformal map to one half of the Einstein static universe is exact, the boundary integral equation can be diagonalized, and the deformed two-point function follows in closed form, $\widehat{\mathcal G}_{\alpha}=\widehat{\mathcal G}_{N}/(1+\lambda\widehat{\mathcal G}_{N})$. Its poles give the normal-mode spectrum, and its determinant gives the free energy exactly within this Gaussian sector. After three local boundary counterterms, the Casimir energy reaches the stability endpoint with a finite square-root cusp. At any finite coupling the bulk $T^{4}$ and $T^{3}$ terms are independent of $\alpha$ and cancel in the difference from Neumann, leaving $\tfrac{\pi}{3}\cot\alpha\,LT^{2}$ as the leading $\alpha$-dependent term. All nonanalyticity comes from one static homogeneous mode, which becomes soft at $\alpha_{\rm crit}$, in agreement with the known classical stability threshold. The susceptibility diverges with exponent $\gamma=1$ and the gap closes with exponent $1/2$. Beyond this angle the mode is tachyonic, and a stable phase would require a stabilizing interaction. In the flat-space limit the physical coupling scales to zero at fixed energy, so the Robin dependence survives only in the soft-frequency sector, which we characterize by a meromorphic Mellin transform in the boost weight. The Robin angle thus gives a control parameter for a Gaussian stability endpoint that can be followed exactly, and raises the analogous question for relaxed boundary conditions in AdS gravity.

The absence of an algebraic relation between the Ricci scalar and the trace of the energy-momentum tensor in Non-Conservative Unimodular Gravity ($\mathrm{NUG}$) opens new possibilities for constructing spacetime geometries from prescribed curvature profiles. Exploiting this property, we develop a curvature reconstruction framework in which traversable wormhole geometries are generated directly from a prescribed curvature profile rather than from the matter sector or the metric functions. The reconstruction procedure is implemented for a power-law Ricci scalar combined with three different redshift functions, leading to distinct classes of static and spherically symmetric wormhole solutions. We investigate their geometrical properties, asymptotic behavior and null energy condition. Although the radial null energy condition remains necessarily violated at the throat, we show that the dimensionless curvature parameter controls the intensity of the exotic matter supporting the wormhole, while the curvature exponent determines the global asymptotic structure of the reconstructed spacetime. In particular, the critical configuration separating asymptotically flat solutions from geometries with residual asymptotic deformation naturally emerges from the reconstruction scheme. These results establish curvature reconstruction from prescribed Ricci scalar profiles as a viable geometrical framework for generating compact-object spacetimes within non-conservative unimodular gravity.

Superconducting circuits (SCs) are the cornerstone of modern quantum technology, enabling scalable computing through coherent control of macroscopic quantum states. Through a legacy that predates modern quantum computing, SCs have emerged as high-precision instruments for discovery. In this review, we highlight the role of SCs as general-purpose quantum laboratories, outlining the emerging landscape of correlated matter-circuit science. We review and unify the capabilities of superconducting quantum hardware across condensed matter, high energy and quantum information sciences. We trace the technical evolution of these architectures, illustrating how their foundational development has culminated in a toolkit for resolving the complexities of macroscopic quantum states.

A long-standing obstacle in quantum turbulence has been the difficulty of sustaining robust statistical steady states, preventing unambiguous identification of universal vortex organization and kinetic scaling. We construct such a steady state in two-dimensional holographic superfluid turbulence by continuous Landau-instability driving, sustaining ${\sim}2500$ vortices free from transient artifacts. The topological charge structure factor $S_c(k)$ reveals Class I disordered hyperuniformity with $S_c(k)\propto k^{\alpha>1}$ as $k\to0$, where $k$ is the wavenumber. This constitutes the strongest long-range order of its kind and its first observation in a strongly driven, far-from-equilibrium quantum fluid with topological defects as the organizing principle, establishing a novel non-equilibrium vortex phase. Exploiting this platform, we resolve the scaling controversy: the apparent $k^{-5/3}$ signature in the kinetic energy spectrum is a narrow crossover between the $k^{-1}$ single-vortex and $k^{-3}$ core regimes, not a genuine Kolmogorov inertial range. The real-space second-order structure function provides decisive evidence via $S_2(r)\propto \ln r$ where $r$ is the spatial separation, with no $r^{2/3}$ Kolmogorov scaling, ruling out a true inertial cascade. These findings reveal that strongly coupled quantum turbulence lacks an inverse cascade due to the absence of macroscopic Onsager clusters, demonstrating energy transport fundamentally distinct from weakly coupled superfluids.

We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.

We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar $\phi^4$ theory in $\mathrm{AdS}_2$, we compute the lowest non-trivial $\mathbb{Z}_2$-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk $\mathbb{Z}_2$ symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the $\mathbb{Z}_2$-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.

In this work, we compute the operator product expansion density for the genus-two handlebody by exploiting its duality with extremal conformal field theories arXiv:0710.2129. Using a Poincaré construction, we analytically determine the first- and second-order corrections in the pinching parameter to the genus-two OPE density through a direct inversion of the partition function. As a consistency check, we also compute the genus-one density within the same Poincaré framework and find perfect agreement with the result obtained from the lightcone bootstrap analysis arXiv: 1906.04184. It is known that, at genus one, the OPE density of extremal CFTs exhibits a negativity pathology for states lying just above the black-hole threshold. We show that this pathology continues to persist at genus two, despite the emergence of a nontrivial inversion kernel. In particular, the OPE density associated with states of both odd and even spin $j_i$ remains negative within a very narrow band above the black-hole threshold. We further analyze the sharp transition from large positive to large negative values of the OPE density across a curve along which the density vanishes.

We study the spread complexity of the infinite-temperature thermofield double state in large-$N$ random matrix theory and investigate the physical meaning of its Lanczos coefficients $b_n$. The leading density of states defines a family of orthogonal polynomials whose recursion coefficients coincide with the Lanczos coefficients of the associated Krylov dynamics. Starting from the Coulomb-gas equation, we derive a pair of nonlinear relations for these coefficients, which we call the Lanczos equations. For normalizable one-cut ensembles, the Lanczos coefficients approach constants at large Krylov index, rendering the asymptotic Krylov chain translationally invariant and the late-time growth of spread complexity linear, with the growth rate given by the spectral average of the group velocity obtained from a Bloch-wave analysis. For an even potential, we further show that the difference between consecutive squared Lanczos coefficients, $b_{n+1}^2-b_n^2$, is the generating function for two-legged maps whose marked legs are separated by the exact geodesic distance $n$. Consequently, the spread complexity acceleration operator equals twice the geodesic generating operator. We illustrate these results in the quartic matrix model, where the expansion in the quartic coupling counts tetravalent planar maps, and in the double-scaled Sachdev–Ye–Kitaev model, where the auxiliary Hilbert space can be identified with the physical chord Hilbert space.

Traversable wormholes in general relativity require non-standard matter sources, making the identification of physically motivated equations of state particularly important. We investigate wormholes supported by a polytropic equation of state, considering homogeneous and inhomogeneous configurations within a unified framework. We derive the corresponding solutions and analyze the effects of the polytropic parameters on the geometry and energy conditions. In the homogeneous case, the polytropic construction yields a consistent wormhole interior whose geometry and matter content are governed by the constant polytropic parameters. For the inhomogeneous case, we obtain a general analytical expression showing that the geometry is completely determined by the radial polytropic coefficient $\omega(r)$. For positive $\omega(r)$, the requirement for physically meaningful solutions naturally restricts the polytropic exponent to odd integer values. Using a power-law profile, we construct explicit classes of solutions exhibiting distinct parameter regimes and finite radial support. Interestingly enough, for an exponent $\alpha=2\gamma-3$, a generalized absurdly benign traversable wormhole-like configuration emerges naturally. Although the flare-out condition implies null-energy-condition violation at the throat, the inhomogeneous framework allows its radial distribution to be controlled. Our results establish a systematic connection between polytropic matter and wormhole geometry, providing a flexible framework for constructing compact wormholes with localized exotic matter.

We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $\epsilon$ on a lattice of volume $V$ at bare coupling $g$ is bounded as $16n_A V + 12n_f V$, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{\pi^2\epsilon} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}\pi^3\epsilon^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy $E'$, and $n_f$ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as $O(n_A^4 V^{4/3}) + O(V^{5/3})$ per Trotter step for fixed $n_f\leq 6$. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.

In this manuscript we derive the $w_{1+\infty}$ algebra on an arbitrary null hypersurface located at finite distance. A straightforward integration of the evolution Bianchi identities is performed in a suitable dynamical reference frame, dubbed the Weyl reference frame. In this reference frame, the extraction of the (linear) higher spin charge bracket is similar to the asymptotic null case, except that the corner metric evolves non trivially in time. In other words, boundary degrees of freedom that are frozen at null infinity due to the boundary conditions now become part of the dynamics. This feature is reflected in the appearance of non-local terms in the brackets. In order to avoid the presence of these non-local terms in the charge bracket, we absorb this non-locality - which encodes nothing other than the history of the corner metric - into the definition of the higher spin charges. Moreover, a new perspective on the memory effect at finite distance is suggested. In conclusion, we believe that this treatment can also be applied to asymptotically (A)dS$_{4}$ spacetimes, where the presence of a non-vanishing cosmological constant leads to the introduction of a cosmological reference frame.

A warped extra dimension in a five-dimensional (5D) anti-de Sitter (AdS) background was introduced in 1999 by Lisa Randall and Raman Sundrum to solve the gauge hierarchy problem in particle physics. As a bonus, a holographic interpretation in terms of four-dimensional (4D) conformal field theories (CFTs) was found. Interestingly enough, another 5D background, linear dilaton (LD), was found to have a holographic interpretation in terms of Little String Theory. In this review, we will show how a set of 5D backgrounds, parametrized in terms of a real parameter $\nu$, generalizes both theories and gives rise, in particular, to AdS for $\nu=0$ and to LD for $\nu=1$. Furthermore, working in the 5D theory, we will consider applications of the LD background to: (i) particle physics, so that the 5D Planck scale can be lowered to sub-Planckian values, and (ii) Brane World Cosmology (BWC), based on the appearance of an extra vacuum characterized by a 5D black hole. In all cases, we find a gapped continuum for bulk propagating fields, which makes a connection with unparticles. In the case of BWC, we also point out the existence of a pressureless holographic fluid that could play the role of dark matter (DM), with feeble (gravitational) interactions with the Standard Model (SM), decoupled from the thermal SM bath, and generated by a freeze-in mechanism after inflation. We also point out the additional possibility of identifying DM with a long-lived, feebly interacting massive graviton, as an isolated resonance generated by radiative corrections to the continuum graviton propagator self-energy.

We investigate the unitarity of quantum evolution relative to an internal time defined by a local observer's clock. The observer is modeled as a relativistic particle carrying both a clock and a matter-field detector, analyzed first on a fixed curved background and subsequently within a fully diffeomorphism-invariant theory of dynamical gravity. In the former case, we find that evolution with respect to the internal clock time is generally nonunitary, implying a violation of the Einstein equivalence principle at the quantum level. In contrast, in the latter case, diffeomorphism invariance allows us to adopt observer-centric coordinates without loss of generality. On the resulting partially-reduced phase space, one of the diffeomorphism generators becomes linear in the clock Hamiltonian, generating a relational evolution that is consistent with the remaining diffeomorphism constraints. Assuming that an effective quantum field theory exists to be consistent with the diffeomorphism invariance, these features ensure unitary evolution relative to the internal clock, thereby preserving the equivalence principle even in the quantum regime. Our results highlight the fundamental role of diffeomorphism invariance in shaping relational unitary evolution from the perspective of a local observer.