Papers

We compute the rate of growth of operator size in matrix models by probing the Lin-Maldacena class of geometries with classical probes. We consider massive point particle probes whose proper momentum equals the size of the gauge invariant operator in the matrix model. We work out the example of the BMN Plane Wave Matrix Model using the electrostatic approach and the method of background fluxes. We also work out complexities in the D2 brane as well as NS5 brane limits of the BMN matrix model along with an example of the irrelevant deformation namely the non-Abelian T-dual of $AdS_5 \times S^5$. Finally, we carry out a possible calculation of the Krylov complexity on the matrix model counterpart by using a simple reduction ansatz known as the pulsating fuzzy sphere model. We outline an algorithm to define Krylov basis elements for the matrix model and compute a few Lanczos coefficients. Our analysis reveals that both the Krylov basis states as well as Lanczos coefficients are uniquely fixed in terms of the mass parameter of the matrix model.

We formulate a first-order thermodynamic description of Jordan-frame tensor–multi-scalar gravity. We derive the exact covariant $1+3$ split of the geometric sector and recast it as an effective imperfect fluid. The interpretation is Eckart-like: effective temperature, conductivity, entropy current, and entropy production are meaningful only on branches where the geometric dissipative variables satisfy matching and integrability conditions. In a generic frame the heat flux is $q_a^{(g)}=-\chi(a_a+W_a)$, with $\chi=-\dot{\mathcal{F}}/(8\pi\mathcal{F})$ and $W_a$ the residual gradient sector. In the $\mathcal{F}$-comoving frame this defines the inertial variable $\chi_{\mathcal{F}}\equiv K_{\mathcal{F}}T_{\mathcal{F}}$, while a nonzero spatial term $W_a^{(\mathcal{F})}$ remains, sourced by scalar directions not aligned with the coupling. Thus the multi-field thermal description is not generically reducible to a single $KT$-type quantity. We derive transport equations for $\chi_{\mathcal{F}}$, for the field-space thermal vector $\chi^A$ and covector $\chi_A$, and for the residual gradient sector. We introduce the diagnostics $\mathfrak D_\chi=\chi_A\chi^A$ and $\mathfrak D_{\rm grad}=\mathcal B_{AB}\mathrm{D}_a^{(\mathcal{F})}\phi^A\mathrm{D}^a_{(\mathcal{F})}\phi^B$. Their meaning depends on the kinetic matrix $\mathcal B_{AB}$: they are canonical contractions when it is nondegenerate, nonnegative norm-like diagnostics only when positive definite, and require extra structure if degenerate. With this qualification, they show that freezing the effective coupling is generally weaker than full relaxation to the GR sector. We construct the entropy current and entropy production in the coupling frame, state the assumptions for nonnegative entropy production, and show that homogeneous cosmology suppresses the spatial sector while retaining nontrivial time-like multi-scalar thermal dynamics.

We develop a reference-renormalized (photon-sphere-free) normalization scheme for Gauss-Bonnet gravitational lensing at finite distance in static, spherically symmetric spacetimes. The method treats the curvature primitive used to reduce the Gauss-Bonnet curvature-area integral as a quantity defined only modulo an additive constant (an additive gauge freedom). We fix this gauge by matching to a physically chosen reference optical geometry in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive $\mathcal{P}_e(r)$ by reference subtraction. The resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical $\alpha$). In asymptotically flat settings the canonical reference is Minkowski, while in Kottler-type backgrounds the canonical reference is de Sitter within the static patch, making the operational fiducial explicit. We validate the method by reproducing Ishihara's finite-distance weak-deflection formulas for Schwarzschild, Reissner-Nordström, and Kottler spacetimes, including the mixed $r_g\Lambda$ term in the Kottler case within the static-patch fiducial. We also present a demonstrative example in which orbit normalization is genuinely inapplicable because no circular null orbit exists in the physical optical region (the Janis-Newman-Winicour spacetime for $\gamma\le \tfrac12$). The result is a unified, geometrically transparent route to finite-distance lensing that preserves compatibility with orbit-normalized prescriptions whenever those apply.

A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the Dirac theory, electrodynamics, and ultimately the electroweak sector of the standard model. We find that coupling the constructed Dirac spinors to electromagnetism yields the correct magnetic moment for charged spin-1/2 particles. Extending electrodynamics to electroweak theory necessitates an algebraic distinction between the structures of the leptonic and Higgs fields not present in the standard model. The conditions of spontaneous symmetry breaking are explored using an alternative representation of weak isospin and hypercharge equivalent to an irreducible representation of $\mathfrak{su}(2)\oplus\mathfrak{u}(1)$ on $\mathbb{C}^4$. This alternative representation disagrees with the standard model on the overall signs of weak neutral currents.

We identify a two-gap complexity structure underlying a holographic obstruction to reaching extremality and to the black-hole-mediated route toward weak cosmic censorship violation. The complexity of formation of extremal AdS black holes diverges logarithmically, while it is finite for every subextremal member of the stationary family. We compute the on-shell Wheeler–DeWitt action of overcharged Reissner–Nordström–AdS in general dimension $D\geq4$. In the minimal prescription, defined by omission of the Maxwell boundary term, the individually divergent Maxwell bulk, on-shell Einstein–Hilbert, and Gibbons–Hawking–York terms cancel exactly. We also evaluate the null–timelike joints and null-boundary counterterms explicitly and show that their combined lower-endpoint contribution vanishes. Adding the Maxwell boundary term produces only a prescription-dependent, regulator-local power-law divergence; no prescription produces a logarithmic divergence, and the corresponding vacuum-subtracted complexity=volume complexity of formation is finite. In the complexity=action and complexity=volume prescriptions, the reverse triangle inequality for complexity distance then implies divergent relative complexity across each adjacent gap. Under a finite-complexity-growth assumption, this gives a conditional obstruction to traversing the stationary path from subextremal black holes through extremality to the superextremal naked-singularity sector.

The memory effect for Robinson-Trautman waves is explicitly worked out. In a first step, we construct the combined frame rotation and coordinate transformation in which Robinson-Trautman waves are manifestly locally asymptotically flat at future null infinity. This allows us to apply well-established results on how to derive the memory effect in this context. In a second step, we construct a suitably improved generalized mass aspect that provides a local Lyapunov function for the flow in the sense that it is manifestly positive. News-free solutions are studied in detail and shown to coincide with the vacuum sector of Euclidean Liouville theory. They correspond to a boosted and rescaled Schwarzschild black hole. As a by-product, we show that the displacement and non-linear memory effects in locally asymptotically flat spacetimes at future null infinity are invariant under supertranslations and covariant under $\mathrm{BMS}_4$ Lorentz transformations and constant rescalings. A novel interpretation of modified flows that control the low harmonics in terms of keeping the system in its instantaneous rest frame is provided.

The interaction of quantum fields with fractal and self-similar geometries encompasses multiple distinct physical regimes, including spectral geometry on intrinsic fractals, macroscopic self-similar Casimir configurations, and bounded Euclidean cavities with fractal boundaries. While the thermal equations of state and spectral asymptotics for these systems are well established, a cohesive treatment of the vacuum trace frequently conflates rigorous mathematical bounds with phenomenological models. In this manuscript, we systematically decouple these regimes and advance a unified effective framework combining the rigorous thermal trace of fractal radiation with a zero-temperature integrated vacuum trace for plate-like self-similar geometries. We demonstrate that for systems governed by a scale-dependent Casimir coefficient $C(d_s, \ln(d/\ell_*))$, the anisotropic stress-energy tensor produces an integrated vacuum trace proportional to its logarithmic running, $\partial_{\ln d}C$. We strictly differentiate this effective macroscopic backreaction from first-principles local trace anomalies on genuine fractal boundaries. Finally, we analyze finite-level ($n$) prefractal realizations, establishing the analytical prerequisites necessary to transition this effective formalism into a quantitatively predictive electromagnetic theory amenable to experimental verification.

Fermion bound states in the background of the 't Hooft-Polyakov SU(2) monopole are investigated for various values of gauge coupling constant $g$, the Higgs self-coupling constant $\lambda$, and the Yukawa coupling constant $y_q$. Numerical solutions to the set of coupled differential equations for various selected points in the parameter space reveal only a zero mode, for which we also present an analytic argument. We show that the monopole profile functions and the zero mode wave function become more localized with increasing $g$ and $\lambda$, while the right-handed component of the latter decreases with $g$. However, as expected, this component increases with $y_q$. We find that the zero mode in the limit $g\to 0$ differs from the zero mode held by the Higgs alone, highlighting the nonlinear and nonperturbative character of the system. Finally, we prove the spectral mirror symmetry of the fermion, whence, together with the existence of the zero mode, we infer the fermion number $1/2$ of the 't Hooft-Polyakov monopole.

In this work, we investigate the optical, dynamical, and radiative properties of an Euler–Heisenberg black hole immersed in a perfect fluid dark matter (PFDM) background. We analyze the photon sphere and shadow, the scalar quasinormal-mode spectrum in the eikonal regime, the grey-body factor through the eikonal QNM correspondence, the sparsity of Hawking radiation, and the corresponding energy emission rate. Our results show that both the black-hole charge and the PFDM parameter significantly affect the photon sphere, shadow size, quasinormal frequencies, Hawking temperature, and emission profile, whereas the Euler–Heisenberg correction is typically subleading in the parameter range explored, although it may become more visible in strong-charge regimes for selected observables. Overall, the dark-matter environment provides the dominant imprint on the phenomenology of the system, indicating that shadow and ringdown-related quantities may serve as useful probes of PFDM effects within the approximations considered.

Classical energy conditions are investigated in generic static and spherically symmetric spacetimes. In setups with nonconstant $g_{tt} g_{rr}$, the appearance of horizons can signal the violation of the null energy condition and the breakdown of some standard near-horizon properties. For configurations satisfying $g_{tt}g_{rr}=-1$, we devise a systematic algorithm to generate solutions of the Einstein field equations that automatically obey the null energy condition. Within this family, we select a particularly significant metric that incorporates a logarithmic correction to the Schwarzschild model and fulfills all standard energy criteria. We examine its main features, including the horizon structure, geodesic behavior, and junction conditions. Our analysis shows that this geometry can be interpreted as an effective exterior description for both horizon-bearing and horizonless compact objects, and suggests that it can potentially act, in certain regimes, as a black hole mimicker.

We review recent progress in string model building in both early and late time cosmology. We describe the main theoretical and phenomenological features of an entire class of inflationary models where inflation is driven by a type IIB Kaehler modulus which enjoys an effective and approximate shift symmetry. We illustrate how reheating can occur via the perturbative decay of the modulus into visible and hidden sector degrees of freedom, paying particular attention to the associated production of axionic dark radiation. We quickly discuss the status of de Sitter vacua versus quintessence model building in string theory, analysing the level of control of these constructions and the main challenges faced by models of dynamical dark energy. We finally present a working model of axion hilltop quintessence in string theory, stressing the importance of initial conditions.

We study the impact of radiation on quantum systems defined by the spins of elementary fermion-antifermion pairs produced at colliders. We present predictions for several processes, showing that energetic final-state radiation can induce decoherence and significantly reduce the entanglement of quantum systems formed by elementary fermion pairs. We investigate the feasibility of observing this effect experimentally in exclusive samples with energetic radiation. A statistically significant signal can be obtained with current data in associated $pp \rightarrow t\bar{t}(g)$ production at the LHC and in $e^+e^- \rightarrow \tau^{+}\tau^{-}(\gamma)$ production at Belle 2. Future electron-positron colliders operated at the $Z$ pole or well above the $t\bar{t}$ production threshold will extend these prospects further.

We present a first study of the scattering process $e^+ e^-\to\pi^+\pi^-\gamma$ beyond next-to-leading order, aimed at providing preliminary insights required for future NNLO predictions for radiative return processes. A complete four-dimensional tensor decomposition of the amplitude is developed, and the associated one-loop polarised amplitudes are evaluated analytically to higher orders in the dimensional regulator, as required for NNLO accuracy. The calculation is complemented by an efficient numerical framework for the evaluation of the resulting five-point Feynman integrals, enabling stable and fast evaluations across the physical production region with evaluation times of a few hundreds of milliseconds. These results are suitable for implementation in Monte Carlo event generators.

We construct cubic scalar field theory on $\lambda$-Minkowski space by combining the Batalin-Vilkovisky formalism with harmonic analysis, and produce two inequivalent noncommutative quantum field theories. The braided theory is based on a braided $L_\infty$-algebra whereby covariance dictates a spectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel'd twist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absence of UV/IR mixing. The standard noncommutative theory is based on a classical $L_\infty$-algebra; in this theory we relate the spectral decompositions into plane wave and cylindrical harmonic eigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and we demonstrate a periodic form of UV/IR mixing in which non-planar correlators are generically ultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

The pulsar beaming fraction is a fundamental quantity for connecting the observed pulsar population to the intrinsic Galactic population and for constraining pulsar emission geometry. In this study, we estimate the beaming fraction in each observational band (radio, $\gamma$-ray, and X-ray) and for each TeV survey (H.E.S.S., HAWC, and LHAASO) using TeV-selected pulsar wind nebulae (PWNe) and unidentified (Unid) TeV sources, assuming that the TeV emission from PWNe is approximately isotropic and that Unid sources are PWNe powered by pulsars whose beams do not intersect our line of sight. Within each survey, the inferred beaming fractions $\sim 0.1-0.3$ are comparable across bands. In contrast, the values differ by more than a factor of two between H.E.S.S. and HAWC/LHAASO. This discrepancy likely reflects survey-dependent selection effects, including differences in angular resolution and energy range, and is also consistent with the possibility that HAWC/LHAASO selected samples preferentially include older pulsars associated with more extended PWNe than those in the H.E.S.S. sample. We further show that the inferred beaming fractions can be reproduced within a unified framework using a time-dependent opening angle, and that this framework remains compatible with the statistical properties of the observed pulsar population.

Fast Radio Bursts (FRBs) are among the most intriguing phenomena observed in radio astronomy. So far, about 130 FRB signals have been confirmed and characterized by different surveys, and the CHIME telescope has recently reported a new catalog of 4539 bursts. Therefore, these numbers are expected to increase in the coming years. The detection, or lack thereof, of lensed FRB events can be used to probe Primordial Black Holes (PBHs) as a fraction of dark matter. We investigate the potential of three upcoming radio telescopes, LOFAR2.0, FAST Core Array, and BINGO, to test the PBH scenario. We forecast that LOFAR2.0 will constrain $f_{\mathrm{PBH}} < 0.16$ for PBH masses $M_{\rm PBH}>1\,{M_{\odot}}$, while FAST Core Array and BINGO will restrict $f_{\mathrm{PBH}} < 0.39$ for $M_{\rm PBH}>10\,{M_{\odot}}$ and $M_{\rm PBH}>10^{-1}\,{M_{\odot}}$, respectively. Despite the existence of stricter constraints, FRB lensing offers an independent and complementary probe of PBHs in the Universe, which will improve in the future.

We revisit the constrained log-subtracted two-point Padé (LSTP) ensemble for thermal $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) thermodynamics in four spacetime dimensions after upgrading the weak-coupling truncation from $\mathcal{O}(\lambda^2)$ to the exact $\mathcal{O}(\lambda^{5/2})$ coefficient. We keep the LSTP interpolation ansatz unchanged and shift the weak-side matching points to the regime where the new term is numerically significant. Within the same parameter scan the admissible set collapses from $9$ nominal survivors ($3$ distinct curves) to a single distinct curve, the crossover range shrinks to a unique value, and the pointwise band width drops to zero within numerical resolution. The Hermite-Padé (HP) central curve does not coincide with the unique LSTP survivor, so the updated weak-side matching removes the LSTP scan uncertainty but not the difference between the two routes. The minimal HP extension that also carries the exact coefficient is uniquely determined and develops a spurious pole-zero pair at small coupling. Away from that pair the HP and LSTP curves still differ, so this difference persists at the same weak-coupling order.

Thermodynamics provides a useful interpretation of scalar-tensor gravity, in which the effective imperfect fluid admitted by the nonminimal coupling features a temperature that is associated with the departure from general relativity. However, in this construction, certain thermodynamical quantities are defined with respect to a particular conformal frame. In the present work, we show that the originally proposed effective temperature assigned to nonminimally coupled scalar field theories is not frame invariant, and can thus be arbitrarily tuned by a change of frame. This raises the question of whether temperature can be viewed as an intrinsic property of a scalar-tensor theory rather than a particular representation of it. Working instead with the frame invariant formulation of scalar-tensor gravity, we find that the frame invariant effective fluid is perfect with identically vanishing temperature. The departure from general relativity is then governed not by temperature, but rather by a frame invariant chemical potential, similar to minimal theories. Therefore, general relativity can be interpreted as a state of diffusive equilibrium for any scalar-tensor theory, regardless of whether it is minimal or nonminimal.

We study projective one-parameter conifold degenerations whose central fiber has finitely many ordinary double points. Existing finite-node theory isolates one rank-one local sector per node on the perverse-sheaf, mixed-Hodge-module, and categorical sides, but does not determine which global extension classes are actually realized by geometry. We show that when the nodes are linked by common cycle geometry or homological relations, the corrected extension is not free nodewise data, but is forced into a smaller relation-controlled subspace. To formalize this, we introduce a cycle-node incidence datum and the associated geometrically realized subspace of the ambient nodewise extension space. Under geometrically admissible and block-adapted incidence hypotheses, we prove that the corrected perverse extension factors through this subspace, with incidence compatibility derived from propagation of local variation data along admissible cycle components, and we show that the same relation law lifts compatibly to the mixed-Hodge-module setting. We then compare this relation law with the resolution and smoothing sides and, in the block-separated cycle family, obtain $R_{\mathrm{res}}=R_{\mathrm{sm}}=R_{\mathrm{ext}}=R_{\mathrm{blk}}$.

Podolsky electrodynamics, a higher-derivative extension of Maxwell's theory characterized by the Podolsky parameter $\lambda=1/m$, which modifies the photon dispersion relation and regularizes short-distance divergences, is investigated. This framework is then coupled to the Carroll-Field-Jackiw (CFJ) model, in which a Lorentz-violating background four-vector is introduced. Within this extended electrodynamics, the photon propagator is obtained in the combined Podolsky-CFJ framework and subsequently applied to Möller scattering. It is shown that the CFJ contribution can reintroduce the short-distance divergence suppressed by Podolsky's term. In the nonrelativistic limit, both the spatial component–which introduces a preferred direction in space and thus breaks isotropy–and the timelike component–which directly affects the dispersion relation–contribute nontrivially to the interaction potential.

Recently, self-dualities based on saddle-point expansions have been proposed as a means to obtain qualitative non-perturbative information in scalar field theories. In this work, we test this proposition quantitatively by studying the phase transition for critical scalar $\phi^4$ field theory in 1+1 dimensions using a variational method. We find that saddle-point methods obtain quantitative agreement for the free energy, but differ on the order of 25 percent for the peak location of the correlation length.

We investigate whether the Starobinsky inflation remains robust after including a minimal scalar extension motivated by the one-loop effective action of scalar-tensor gravity. We numerically solve the four-dimensional background system derived from the reduced slow-roll action and discover that the exact Starobinsky branch is a finite-time attractor in the sampled slow-roll domain when the additional scalar is at least as heavy as the scalaron. We derive quadratic actions for tensor and scalar modes and find a healthy kinetic sector with no scalar or tensor gradient instabilities. The propagation speeds are indistinguishable from the speed of light over the tested range of the derivative-coupling coefficient. These stability tests use the complete constraint-reduced quadratic operator over $|\beta|\leq1$, whereas the quoted production curvature spectra are obtained from the reduced scalar evolution. A direct complete-spectrum comparison in $\beta$, a separate complete–reduced regression at $\beta=0$, and independent bounds on the canonically normalised coefficient differences constrain the omitted derivative-coupling correction, including the numerical and CPU–GPU allowances, to at most $3.89488834\times10^{-7}$, below the $10^{-3}$ accuracy relevant to the physical conclusion. The curvature spectra remain extraordinarily close to the Starobinsky model across the entire parameter scan. Although the entropy-seeded mode can provide approximately one quarter of the final curvature power, removing the adiabatic–entropy mixing changes the total spectrum by only a few parts in a million, revealing nontrivial multifield dynamics behind an exceptionally robust observable prediction.

We study a boost-invariant, out-of-equilibrium fluid of non-interacting Dirac fermions with a finite canonical spin potential. After solving the Dirac equation in Milne coordinates, we exactly diagonalize the non-equilibrium density operator and compute the partition function and expectation values of relevant observables, including spin polarization, energy density, longitudinal and transverse pressures, spin density, and spin torque, i.e. the source of spin non-conservation. We find an analytic expression for the partition function at finite spin potential, and show numerically that thermodynamic relations connecting it to thermodynamic functions hold in the system under consideration. We show that, in a boost-invariant system, both shear-induced polarization and the spin Hall effect are absent, and that a non-vanishing polarization can only arise from a finite spin potential in a free theory. We obtain an analytic expression for the spin polarization as a function of the spin potential in some particular cases, and otherwise compute numerically its exact expectation value at finite spin potential. Our results are discussed in the context of relativistic spin hydrodynamics and quark–gluon plasma phenomenology.

We investigate the properties of neutral and charged mesons in magnetic fields, from weak-field to strong-field regimes. To develop analytic insights, we employ a non-relativistic quark model with a confining potential of the harmonic oscillator type. Short-range correlations, such as Coulomb and color-magnetic interactions, are treated as perturbations. In particular, we focus on the magnetic field dependence of the relative and the center-of-mass motions. The qualitative trends differ significantly between neutral and charged mesons: for neutral mesons, the transverse momenta are conserved and continuous, while charged mesons exhibit quantized transverse dynamics. The Zeeman effects, arising from intrinsic spins and orbital angular momenta, are carefully examined. In particular, for charged mesons with spins $s\ge 1$, we discuss how the zero-point energy in the internal quark motion cancels the Zeeman energy from the orbital angular momentum, ensuring the energetic stability of mesons with high spins. The effectively reduced dimensionality of these mesons in the strong-field limit is also discussed.

The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented $S=1$ dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.

We compute the efficiency of the reversible Stirling engine, with and without regeneration, for a broad class of working substances including Van der Waals fluids, quantum ideal gases (Bose and Fermi), Bose-Einstein condensates, thermal conformal field theories (CFTs), and holographic CFTs. Regeneration acts as an internal heat recycling mechanism that enhances efficiency by reducing the net heat exchange with external reservoirs. For regenerative Stirling cycles, we identify a general sufficient condition for attaining Carnot efficiency: at fixed conserved charges, the fixed-volume heat capacity is independent of volume. This ensures that, at each temperature along the isochores, the heat released during cooling equals the heat absorbed during heating. An ideal regenerator can therefore store and return this heat reversibly, returning to its initial thermodynamic state with no net change in energy or entropy. While this condition is satisfied for classical ideal gases and Van der Waals fluids, it is violated for quantum ideal gases and CFT working substances. For thermal CFT states dual to AdS-Schwarzschild and AdS-Reissner-Nordstrom black holes, we obtain exact expressions for the Stirling efficiency. In the fixed-potential ensemble, both the regenerative and non-regenerative efficiencies approach the Carnot value in the large-potential limit. Regeneration reduces the leading deviation from the Carnot value, although both efficiencies have corrections of the same asymptotic order.

We study a simple theory based on general relativity, minimally coupled to a constrained scalar triplet and to an auxiliary non-propagating three-form sector. Within a spherically symmetric hedgehog ansatz, the theory admits a continuous exact family of asymptotically flat geometrically regular black holes. For a simple choice of kinetic function, the solutions possess a de Sitter core and approach Schwarzschild with the first correction appearing only at order $r^{-4}$. We analyse their horizon structure, thermodynamics, and main strong-field properties. The black holes carry topological scalar hair and a continuous secondary parameter, but no scalar charge. The regularity established here is geometric: the curvature invariants remain finite, although the matter sector is not completely smooth at the centre.

Non-commutative electrodynamics obtained through the Seiberg-Witten map ceases to have equivalent action-level and equation-level realizations once fixed external currents are introduced, and in the action-level construction associated with the Banerjee current map the canonical location of this source-induced obstruction has remained unclear. Working in the full phase space and treating the current as prescribed and non-dynamical, we apply the Dirac-Bergmann algorithm without imposing current conservation as an external condition. The preservation of the Gauss-type secondary constraint produces a third-stage candidate whose phase-space expression is shown to be algebraically identical, at first order in the non-commutativity parameter and for purely space-space non-commutativity, to the canonical pullback of the divergence of the mapped Euler-Lagrange equations. This identity locates the source-compatibility obstruction directly within the Dirac chain. For generic inhomogeneous sources, the next consistency step feeds this object back into the primary multiplier through a source-dependent kernel, so the chain closes by multiplier fixing rather than by the generic appearance of a quaternary constraint. Reduced-phase-space results, including the gauge generator, Dirac brackets and degree-of-freedom count, are obtained only in a restricted sufficient first-class subcase; no broader claim is made for arbitrary source profiles.

In finite-width deep neural networks, the empirical kernel $G$ evolves stochastically across layers. We develop a collective kernel effective field theory (EFT) for pre-activation ResNets based on a $G$-only closure hierarchy and diagnose its finite validity window. Exploiting the exact conditional Gaussianity of residual increments, we derive an exact stochastic recursion for $G$. Applying Gaussian approximations systematically yields a continuous-depth ODE system for the mean kernel $K_0$, the kernel covariance $V_4$, and the $1/n$ mean correction $K_{1,\mathrm{EFT}}$, which emerges diagrammatically as a one-loop tadpole correction. Numerically, $K_0$ remains accurate at all depths. However, the $V_4$ equation residual accumulates to an $O(1)$ error at finite time, primarily driven by approximation errors in the $G$-only transport term. Furthermore, $K_{1,\mathrm{EFT}}$ fails due to the breakdown of the source closure, which exhibits a systematic mismatch even at initialization. These findings highlight the limitations of $G$-only state-space reduction and suggest extending the state space to incorporate the sigma-kernel.

We investigate the stringy effects on holographic complexity in $(d+1)$-dimensional Gauss-Bonnet gravity using the “complete volume” proposal for higher-curvature theories. Our analysis covers unperturbed eternal black holes, as well as the one-sided and two-sided Vaidya spacetimes. The one-sided geometry describes a null shell collapsing into the empty AdS vacuum to form a black hole, while the two-sided geometry represents a null shell injected into an eternal black hole background with arbitrary energy. For unperturbed backgrounds, higher-curvature terms introduce explicit corrections to the standard CV proposal, giving rise to a “competition effect” absent in the uncorrected framework. In the dynamical settings, we demonstrate that despite novel jumps in the canonical velocities across the null shell, the complexity growth rate remains universally governed by the conserved momentum, just as in Einstein gravity. Furthermore, our two-sided shock wave analysis reveals that Gauss-Bonnet corrections prolong the critical time, preserving the universal logarithmic dependence for the scrambling time.