Papers

We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.

We study the two-dimensional Ising model deformed by the relevant thermal operator and placed on de Sitter (dS) spacetime. Despite being strongly interacting in its original formulation, the theory is exactly solvable on account of fermionisation. We compute exact cosmological correlators and compare them with conformal perturbation theory. In the Euclidean formulation of the model, we first compute the renormalised sphere partition function and the exact two-point functions of the thermal operator and descendant-like operators. We analytically continue the two-point functions to Lorentzian dS$_2$. Their late-time behaviour is governed by de Sitter representation theory and includes oscillations associated with principal-series scaling dimensions. We then analyse two-point functions of the spin and disorder operators, which are non-local in the fermionic variables, and derive non-perturbative constraints on their late-time scaling dimensions. In both cases, we compare the exact answers to conformal perturbation theory (CPT) and we show that divergent secular terms generically spoil the perturbative series at late times. The de Sitter Ising model shows explicitly how late-time perturbative pathologies are resummed in non-perturbative cosmological observables and provides a minimal solvable laboratory for quantum field theory dynamics in de Sitter space.

The de Sitter horizon behaves in a qualitatively different way from a black hole horizon, which poses a challenge to any attempt to develop a fundamental quantum description of de Sitter space. In this paper we gather some “data” on this problem using gravitational calculations, seeing that they lead to an “anti-scrambling” phenomenon that is contrary to the behavior of standard many-body quantum systems. We organize our discussion in terms of correlation functions computed on the worldline of an observer living in the spacetime, with the two-point function looking like a conventional thermal correlator but the four-point function showing anti-scrambling. We propose that anti-scrambling can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.

Motivated by the problem of understanding the experience of an observer in dynamical quantum gravity, we study the effects of coupling a one-dimensional quantum mechanical system living on a bulk worldline to Euclidean AdS JT gravity. On the disk topology, where the worldline stretches between two boundary points, we derive exact expressions for the Euclidean propagator of the observer and for its correlation functions, and discuss their holographic interpretation. The main effect on the quantum mechanics is the fluctuation of the total Euclidean time for which the observer evolves, or its inverse temperature for closed Euclidean paths. This turns the standard quantum mechanical evolution operator into an average of those, weighted by a measure over Euclidean times which in the semiclassical limit is peaked around the geodesic distance between the boundary points. We characterize the fluctuations around this value, finding that they are small compared to the mean, but large compared to the effective Planck scale of the model. These fluctuations can be resolved by an observer with a finely spaced density of states. We also discuss the Lorentzian interpretation of these Euclidean calculations. Finally, we compute a contribution to the partition function of the observer coupled to gravity coming from the double trumpet. In this case the fluctuations of the effective temperature are large, reflecting the absence of a smooth semiclassical saddle point.

We investigate the thermodynamic and observable signatures of thin accretion disks surrounding rotating, regular Hayward black holes embedded within a macroscopic dark matter (DM) envelope. The spacetime is rigorously modelled as a three-region composite: an inner Hayward core regularised by a de~Sitter limit, an intermediate DM shell modelled as a pressureless dust envelope governed by an exponential sphere density profile, and an asymptotically flat outer vacuum. By matching these regions via the mass profile, we compute the explicit modifications to the Innermost Stable Circular Orbit (ISCO), radiative efficiency, local thermal flux, and multi-colour blackbody spectral luminosity. A systematic comparison across four distinct configurations (Kerr vacuum, Hayward vacuum, Kerr\,+\,DM, and Hayward\,+\,DM) reveals a strict hierarchical compression of the ISCO. We demonstrate that the quantum-inspired core regularity and the macroscopic DM halo exert an additive enhancement on the radiative efficiency, reaching $\sim 14.4\%$ for highly spinning black holes ($j=0.8$). However, this additive behaviour introduces a profound macroscopic degeneracy between purely geometric (Hayward vacuum) and purely astrophysical (Kerr\,+\,DM) configurations at low-to-intermediate frequencies. We establish that this degeneracy is structurally broken only in the extreme Wien tail of the multi-wavelength spectrum, providing a critical diagnostic footprint for future high-frequency spectropolarimetry to distinguish non-singular black holes from classical dark matter environments.

The classical formation of a Schwarzschild black hole from a regular, non-singular configuration has recently been shown to be impossible within general relativity: the geometry inevitably develops a discontinuity at the origin, a phenomenon termed Minkowski breaking by Ovalle, Casadio, and Kamenshchik [PRD 113 (2026), 064042]. This obstruction signals that the transition to the Schwarzschild point mass must be a discrete, quantum event. We uncover the thermodynamic footprint of this transition. Using the explicit family of regular Schwarzschild black holes with a de Sitter core, we show that the inner Killing horizon carries a formal Bekenstein-Hawking entropy $S_{\rm inner} = A_{\rm inner}/4$ that is absent in the singular Schwarzschild state. This entropy is hidden from external observers in equilibrium but, assuming the generalized second law, must be released when the inner horizon disappears. As the collapse parameter $n$ decreases, the inner horizon shrinks and its entropy is gradually released during classical evolution, until the horizon finally vanishes at $n=0$ with the Minkowski breaking. The surface gravity diverges as $n\to0^+$, with the semiclassical description breaking down at $n \sim 1/\ln(h/\ell_P)$; the final disappearance is therefore a deep quantum process. For the $n=3$ regular black hole, the stored entropy is approximately $59\%$ of $A/4$; in the semiclassical limit $n\gg1$, it approaches the full $A/4$. The integer nature of $n$ implies a quantized entropy spectrum, with the Schwarzschild black hole as the ground state within the OCK family. We discuss how the classical mass-inflation instability may be circumvented by the quantum disappearance of the Cauchy horizon, and clarify the continuous vs. discrete nature of the collapse.

We study a version of de Sitter static patch holography in which the Euclidean gravitational path integral, with an observer worldline included, is conjectured to compute a trace. Motivated by recent evidence for this conjecture from the sphere path integral, we test it further by inserting operators along the observer worldline and computing two-point functions and out-of-time-ordered four-point correlators (OTOCs). We extend an earlier OTOC calculation by Kolchmeyer and Liu using the shockwave formalism, incorporating both observer recoil and gravitational backreaction. We find that the OTOC conflicts with two basic properties of a trace in a Hilbert space: cyclicity and positivity. The signaling feature of the shockwave geometry gives rise to two distinct resummations of the perturbative eikonal expansion, which are interchanged by cyclicity. Positivity is violated by the fact that the leading perturbative contribution causes the (regularized) OTOC to increase.

Lambert series of the form $\sum_{n>0}a(n)q^n/(1-q^n)$ are ubiquitous in mathematical physics. In particular, 2-loop sunrise and 3-loop banana Feynman diagrams yield Lambert series with $a(n)$ of the form $\chi(n)/n^s$ where $\chi(n)$ is a Dirichlet character. Resurgence concerns the singular limit as $|q|$ approaches 1. In the Feynman cases we can control this limit, obtaining rapidly convergent expressions, since the Lambert series are iterated integrals of holomorphic Eisenstein series twisted by a character. We generalize this result, to include modular resurgent structures found in topological-string observables.

We formulate timelike entanglement entropy and its Rényi extension in two-dimensional conformal field theory through the analytic continuation of replica twist correlators to time-ordered, timelike-separated insertions. This field-theoretic construction grounds and generalizes recent developments, and applies to temporal subregions of arbitrary extent. Within three-dimensional holography, the semiclassical boundary correlator identifies boundary-anchored complex geodesics as the relevant bulk saddles and selects the one with the smallest real part of the length. This provides a direct boundary derivation of the proposed complex extremal surface prescription and extends to Rényi index $n>1$, for which we explicitly construct the corresponding complex cosmic brane geometry in the vacuum. We develop these ideas in several representative settings, including locally and globally excited states and quantum operator quenches, making manifest the precise agreement between boundary twist correlator and bulk complex geodesic calculations. For AdS-Vaidya, our approach predicts a different result from earlier piecewise geodesic constructions, while reproducing the field theory answer. Across these examples, the operator ordering uniquely determines the imaginary part of the complex-valued entropy, which is quantized in units of $c\pi/6$ and sensitive to the effective causal structure but not to the underlying dynamics.

We investigate the origin of the ultra-high-energy $\gamma$-ray emission detected by the Large High Altitude Air Shower Observatory (LHAASO) from the source LHAASO J0341+5258, which has not yet been associated with any known astrophysical object within the detector's field of view. The observed UHE emission is modelled within two independent frameworks: initially with a time-dependent, source-independent hadronic scenario implemented with the numerical package GAMERA, where particles propagate through the interstellar medium and subsequently interact with the molecular gas observed in the region and finally with an analytical description of the interaction between the accelerated cosmic-ray population from a supernova remnant (SNR) and the molecular gas around it. The relevant parameter space for the hypothetical past SNR is explored using the observed TeV $\gamma$-rays. We show that, for physically plausible source-cloud separations and propagation timescales, GAMERA provides a first-order approximation to the spectral modifications induced by particle transport and yields an adequate fit to the ultra-high-energy $\gamma$-ray data. Within the framework of our analytical approach, we demonstrated that the observed GeV emission can plausibly originate from the SNR itself, while the TeV emission detected by LHAASO can be consistently interpreted as arising from particles that have escaped from the SNR and are illuminating nearby molecular clouds. We invoke a spatio-temporally evolved SNR-molecular cloud interaction scenario to account self-consistently for the entire $\gamma$-ray spectrum from GeV to TeV energies. Despite the remaining uncertainty regarding the nature of the acceleration source, we conclude that the TeV emission detected by LHAASO can be consistently interpreted within the framework of an illumination scenario.

We present fixed-order perturbative calculations up to four-loop order for a generic non-global QCD observable in hadron-hadron collisions. Specifically, we study the invariant-mass distribution of the highest-$p_t$ jet produced in association with a vector boson or a Higgs boson, where jets are defined using the Cambridge/Aachen sequential recombination algorithm. This work is part of a series of papers~\cite{Khelifa-Kerfa:2015mma, Khelifa-Kerfa:2024hwx, Khelifa-Kerfa:2024dut, Khelifa-Kerfa:2025cdn, Khelifa-Kerfa:2024udm, Khelifa-Kerfa:2025jev} examining the impact of various jet algorithms on the perturbative structure of non-global observables across different collision environments. We find that at fixed order the Cambridge/Aachen algorithm suppresses the large non-global logarithms more effectively than the anti-$k_t$ and $k_t$ algorithms, while at all orders it performs comparably to the $k_t$ algorithm. Furthermore, comparisons of all-orders resummed form factors reveal that finite-$N_c$ corrections remain at the percent level, consistent with previous findings.

First, for orbifolds of Calabi-Yau threefolds of Fermat type, we define Roan's Hodge numbers. We prove, Theorem \ref{main} , that for all orbifols of Calabi-Yau threefolds Fermat type, Roan's Hodge numbers correctly count the stringy Euler numbers due to Vafa formula. Second, for Calabi-Yau threefolds Fermat type, we apply Roan's Hodge numbers to get a relation between the Borcea-Voisin construction \cite{Borcea, Voisin} and Berglund-Hübsch-Krawits mirror symmetry (BHK mirror symmetry). Third, for orbifolds of K3 surfaces Fermat type, we establish relations twisted and untwisted parts of the second mixed cohomology to deformations and the Roan pairs. This allow us to confirm the BHK mirror symmetry for such orbifolds, since the Euler numbers computed by the Vafa formula are equal $24$ for all of them.

We investigate the radiative generation of the Carroll–Field–Jackiw (CFJ) term in nonlocal Lorentz- and CPT-violating extensions of quantum electrodynamics. Nonlocality is introduced in the fermionic sector through entire form factors depending on the Dirac operator. Using the Fréchet and derivative expansions of the one-loop fermionic determinant, we derive the induced CFJ contribution and analyze its ultraviolet behavior after Wick rotation. For one class of form factors, the loop integrals are absolutely convergent at finite nonlocality scale $\Lambda$, without requiring an additional UV regulator. For another class of form factors, the CFJ coefficient is defined through an Abel regularization prescription. In both cases, the CFJ structure is preserved and its coefficient is continuously modulated by the ratio between the fermion mass and the nonlocality scale. Thus, nonlocality removes the routing-, surface-term-, and UV-evanescent ambiguities of the finite-$\Lambda$ loop amplitude, although UV convergence alone does not imply complete prescription independence of the finite functional determinant.

Cosmologically coupled black holes (CCBHs), whose masses evolve in response to the cosmological expansion, have recently attracted significant theoretical and observational interest. Existing studies have treated CCBHs as purely classical objects, neglecting the effect of Hawking radiation (HR), which competes with the cosmological coupling (CC) mechanism. We take a first step towards studying evaporating CCBHs, adopting a quasi-adiabatic approximation in which the HR rate is evaluated at the instantaneous CCBH mass, and modeling the CC mechanism through the phenomenological scaling of the mass with the scale factor, $M \propto a^k$. We show that, depending on the coupling strength $k$, even late-time CC activation can significantly delay Hawking evaporation, or lead to asymptotic CC-dominated mass growth, with important implications. We set limits on the abundance of primordial CCBHs from $\gamma$-ray observations, finding limits which are weaker than their uncoupled counterparts, as CCBHs are kept farther from the endpoint of evaporation for a longer time. Unlike standard primordial black holes, the CCBH formation and present-day masses no longer approximately coincide, even for formation masses $M_{\text{form}} \gtrsim 10^{15}\,{\text{g}}$. Therefore, the same population of primordial CCBHs may be subject to evaporation limits through its past emission history, as well as to other limits (such as microlensing) through its present-day mass.

In this work we formulate a horizon-microstructure description of four-dimensional AdS black holes in which a horizon of area $A$ is resolved into $\mathcal{N}=A/a_p$ microscopic sites and $N$ occupied horizon sites. The central result is that the combinatorics of this partially occupied horizon sector yields the entropy directly: in the finite-filling regime the leading term is proportional to the area, and the maximal-entropy filling reproduces the Bekenstein–Hawking law with $a_p=4\ln 2\ \ell_{p}^{2}$. Subleading corrections include a subtractive logarithmic term and an inverse-area expansion. We then show that this partially occupied regime admits a thermodynamic justification from an extended first law with chemical potential $\mu$, a Smarr-consistent excitation enthalpy $\delta M(A,P,N)$, and an AdS control parameter $u=PS$. In this interpretation, the combinatorics provides the dominant horizon entropy, while the thermodynamic sector supplies a dressing that selects the equilibrium filling and assigns a finite excitation cost to departures from a reference partially occupied configuration.

We formulate quantisation of gauge field theories on globally hyperbolic Lorentzian manifolds with marked hypersurfaces within the framework of perturbative algebraic quantum field theory (pAQFT) enriched by the Batalin, Fradkin, Vilkovisky formalism (BV/BFV). This allows one to incorporate some crucial aspects of the local functorial approach to gauge field theory on manifolds with boundary within the algebraic setting. In particular, we provide a pAQFT-formulation of the modified classical and quantum master equations (after Cattaneo, Mnev and Reshetikhin CMR), as well as a constructive way to build a renormalised quantum BFV operator correcting the failure of the Quantum Master Equation by means of boundary terms (in the appropriate sense). We find that the renormalised quantum homotopy dg Lie algebra arising from the Anomalous Master Ward Identity becomes curved when boundaries are considered. The failure of the quantum master equation is thus encoded by a nontrivial curvature term in an $L_\infty$ algebra. As a byproduct, we recover previous results of Hollands' on the relation between the (boundary) BRST charge and the BV operator, and we recover CMR's ansatz for the quantum BFV operator at leading perturbative order on causal cylinders in Abelian Yang–Mills theory.

Matrix models appear as fundamental descriptions of M-theory and D-brane dynamics, and via the gauge/gravity duality their gauge-invariant, or singlet, sector describes the purely gravitational degrees of freedom in the holographic dual. We present a new exact algorithm for computing observables of bosonic U(N) matrix models in the gauge-invariant singlet sector. This sector is spanned by an orthogonal basis of Schur polynomials (for a single matrix) and restricted Schur polynomials (for multiple matrices), which diagonalizes the free Hamiltonian and provides a natural truncation of the Hilbert space by excitation number. Matrix elements of the interaction Hamiltonian, or any gauge-invariant observable, are evaluated through a group-theoretic reduction to cosets and double cosets of suitable subgroups of the symmetric group, together with character sums on the symmetric group. The resulting entries are closed-form polynomials in the gauge-group rank N, assembled from group-theoretic data that are precomputed once and can be reused for any N and any coupling constants. We validate the one-matrix implementation against the exact mapping to N non-interacting fermions, demonstrating rapid convergence of the low-lying spectrum with the cutoff. The multi-matrix extension is outlined; its main bottleneck is the computation of restricted characters of the symmetric group, for which no algorithm comparable to the Murnaghan–Nakayama rule is currently known. The framework gives direct access to finite-N, finite-coupling dynamics of gauge-invariant states and opens a new computational window on the non-planar regime of holographic matrix models.

The mirror Thermodynamic Bethe Ansatz (TBA) describes the spectrum of $\text{AdS}_3\times\text{S}^3\times \text{T}^4$ superstrings supported by a mixture of Ramond-Ramond (RR) and Neveu-Schwarz-Neveu-Schwarz (NSNS) flux. In recent years, a conjecture was put forward regarding the Quantum Spectral Curve (QSC) formulation in the Ramond-Ramond case. In this paper, we initiate the derivation of the Ramond-Ramond QSC from the mirror TBA equations. We describe the Y-system underlying the TBA and its discontinuity relations for pure-RR backgrounds. This provides the foundation for the derivation of the T-system and the Quantum Spectral Curve, which will be presented in a follow-up paper.

We study the algebra of observables of a semiclassical observer in de Sitter space. When operators are time-evolved by a scrambling time, out-of-time-ordered correlation functions (OTOCs) receive corrections due to shockwave scattering near the cosmological horizon. When the observer's clock is treated classically, we show that the time advance effect implies the breakdown of the KMS condition for vacuum correlators of matter operators. When the observer's clock is quantized, this implies that the Hartle-Hawking state is not a trace on the resulting crossed-product algebra. We conjecture that the observer's algebra has a trivial commutant. When the time separation between operators exceeds the scrambling time, the OTOC decays to zero and a free product algebra emerges. We illustrate this using classical solutions of de Sitter JT gravity with shocks. We comment on how our results pose a challenge for observer-centric static patch holography.

We numerically study kink-antikink collisions in the self-gravitating $\phi^4$ model coupled to the two-dimensional dilaton gravity theory proposed by Mann et al. The static kink solutions interpolate between an anti-de Sitter (AdS$_2$) region and a Minkowski region, and can be regarded as two-dimensional analogues of certain thick branes. By scanning the initial velocity for several gravitational couplings, we find that gravity modifies the scattering structure: the resonance windows shift toward higher initial velocities and become progressively narrower as the coupling $\kappa$ increases, while the critical escape velocity increases mildly. A linear perturbation analysis further indicates that the shape modes turn into long-lived quasi-bound states in the weak-gravity regime, which could leak energy during collisions and may therefore contribute to the shift and narrowing of the windows and the increase of the critical velocity. The collisions further produce a clear geometrical response: the conformal factor decreases after the collision, corresponding to a contraction of the local proper spatial scale in the conformal gauge, and this effect becomes stronger for larger $\kappa$. Meanwhile, the Ricci scalar develops transient peaks during kink encounters but remains finite in all simulations considered. Thus, in contrast to higher-dimensional thick-brane collisions, we find no evidence for spacetime singularity formation in this two-dimensional model.

We extend the recently established framework of Lorentz-covariant relaxation bounds from linearized classical kinetic and rheological theories to the full quantum setting of thermal quantum field theory (QFT). Working directly with retarded two-point functions at finite temperature and density, we show that the analyticity and positivity properties of spectral functions – combined with Lorentz covariance and the Kubo–Martin–Schwinger (KMS) condition – impose rigorous frame-dependent constraints on the location of singularities in the complex frequency plane. Specifically, we prove that the non-hydrodynamic quasinormal spectrum in any boosted frame is confined to a strip whose width is determined solely by the rest-frame spectral weight at zero spatial momentum and the maximal group velocity of the theory. We derive covariant sum rules for the spectral density under Lorentz boosts and establish that the convergence radius of the hydrodynamic gradient expansion transforms in a manner dictated by the same rest-frame data. In holographic theories dual to Einstein gravity in asymptotically anti-de Sitter spacetime, we verify the bounds by an explicit quasinormal-mode computation: the leading boosted pole moves deeper into the complex plane – the observed relaxation rate increases with boost velocity, in sharp contrast to naive time dilation – while respecting the bound throughout; we further derive corrections from higher-derivative gravitational terms. Our results provide a first-principles, non-perturbative derivation of Lorentz-covariant spectral constraints applicable to the quark-gluon plasma, superfluid phases of neutron star matter, and strongly correlated electrons near quantum critical points.

An inverse problem comprises a matrix equation together with its unknown space, physical data, equivalence relation, and validation tests. We formulate Bern–Carrasco–Johansson (BCJ) numerator construction as an exact adaptive inverse problem. A fixed scientific specification determines the theory, graph conventions, coefficient field, locality and power counting, cut data, observable equivalence, and independent checks. Each finite working specification compiles to $\mathcal{P}_\sigma=(A,b;\mathcal{S};\mathcal{T})$, where $Ax=b$ reconstructs numerator coefficients, $\mathcal{S}$ classifies the solution fiber, and $\mathcal{T}$ tests it on held-out information. Left-null obstructions identify candidate numerator-basis directions needed for consistency, while the action of candidate measurements on the right kernel identifies informative new cut equations. We illustrate these steps by hand at four points and apply them to one-loop five-gluon pure Yang–Mills theory. After kinematic and graph-symmetry reduction, the candidate numerator basis contains 1127 independent coordinates. The combined maximal, box, triple, and double cuts have rank 920, giving a 207-dimensional affine solution fiber. Exact reconstruction determines a particular solution and the complete ordered kernel. The specified $R_{12345}$ color-ring readout $\mathcal{S}$ annihilates every kernel direction, so the full fiber represents one observable class. A published forward-limit numerator lies in this fiber, and fresh cuts, independent integral reductions, and helicity-amplitude benchmarks validate the result. Explicit search rules and agent interfaces can propose revisions. Deterministic compilation and exact evaluation assess each proposal.

By viewing scattering amplitudes as computer programs, we connect two goals: exposing useful analytic structure and constructing efficient numerical evaluators for collider phenomenology. Equivalent programs can differ sharply in multiplicity scaling, arithmetic complexity, cancellation, and runtime. Amplitude calculation therefore defines a structured search problem over analytic representations, recursive algorithms, colour and helicity organisation, and reuse of intermediate objects. We embed repository-scale coding agents inside an external generate-evaluate-select loop with frozen evaluators and objectives, and study three optimisation targets. A scaling search moves from BCFW recursion to a specialised fixed-k split-helicity transfer algorithm, reaching an 805x geometric-mean speed-up on the scored grid. A structural search reorganises NMHV terms into R-invariant-style cells and glued supercells, reducing inter-term cancellation. Across twenty QCD and electroweak processes, an exact-operation search reduces counted arithmetic by 47.7x and gives a 5.9x post-hoc Python runtime improvement. In matched pure-gluon component tests from n=4 to n=6, the evolved engine's speed advantage over the tested Sherpa-Comix exact-sum call grows from 10x to 277x, while its gap to process-specialised MadGraph5_aMC@NLO Fortran compiled at -O3 narrows from 77.7x to 13.7x. The searches move between mathematical representations and combine recursion, symmetry, basis reduction, dynamic programming, and shared computation into hybrid amplitude programs. They provide initial evidence that parts of amplitude optimisation can be made systematic through self-evolving program search, while leaving native generator integration and end-to-end event throughput as future tests. The generator comparison is an isolated exact matrix-element call, not a modification of MadGraph or Sherpa.

In this work, we have performed the theoretical estimation of the lowest boundary of an axion mass. We have analyzed the energy spectrum of the electron in a constant homogeneous magnetic field, taking into account its anomalous magnetic moment. We have applied the obtained results on the energy spectrum of the electron in a constant homogeneous magnetic field with allowance for its anomalous magnetic moment to the hydrogen atom electron, which is located in addition to the Coulomb field of the proton, as well as in the magnetic field produced by the magnetic moment of the proton. We have applied the idea of the restriction for the lowest boundary of the axion mass to the triplet-singlet transition between two adjacent levels obtained as a result of the hyperfine structure splitting of the s-levels in the hydrogen atom. We have concluded that the mass of an axion ought to be more than 5.885 microelectron-Volt. We have determined that the minimum value of the magnetic field strength at which the axion emission by the electron in a magnetic field starts to be realized is determined by the axion mass. This result enables us to estimate the expected value of the lowest boundary for the axion mass (of the order of 10 microelectron-Volt), assuming that some part of the solar axions is emitted by the electrons located in sunspots.

We derive generalized effective Friedmann and Raychaudhuri equations for a bouncing polymer quantized Bianchi-I spacetime. We further prove that the relation numerically derived in the literature between the matter energy density and the anisotropic shear at the bounce holds exactly for any type of matter content, and derive explicit expressions for the constants that appear in that relation.

The worldline approach to quantum electrodynamics allows one to construct integral representations combining large numbers of Feynman diagrams. Here I review the state-of-the-art of a long-term effort to make this fact useful for actual multiloop calculations, such as of the scalar and spinor QED vacuum polarization functions and the electron anomalous magnetic moment. After a short historical introduction, and a discussion of the non-standard mathematical challenges involved, I focus on a recent calculation of the two-loop vacuum polarisation in scalar QED and some master integral formulas obtained in this context.

We develop a local spectral framework for the Landau-gauge Gribov horizon that distinguishes gauge-orbit projection from degeneracy of the gauge-fixing Hessian. On a flat torus, spatially constant ghosts form a residual global-color kernel; after removal of this kernel, the reduced Faddeev-Popov operator is the normal Morse-Bott Hessian of the orbit-norm functional, whereas the covariant Laplacian defines the orthogonal connection. For the associated affine focal pencil, we prove a quadratic-form index theorem with a Morse-Bott endpoint. At a regular isolated crossing, the critical projector $P$ and invertible compressed derivative $\Gamma=P\dot{\mathcal{M}}P$ determine the spectral-flow jump and leading Laurent coefficient of the sourced ghost resolvent; for a simple zero, they also give the wall conormal. Crossings reached along affine rays from the positive region have negative-definite $\Gamma$, including symmetry-protected multiplets, while a second Schur reduction determines pole orders along tangential paths. A projected single-harmonic model checks the projected Feynman-Hellmann relation. For an $SU(2)$ hedgehog on $\mathbb R^3$, we construct a normalizable threshold state in every coupled spin-orbit channel and minimize over the full tower to obtain the exact stability interval $-2<g<1$. Dirichlet-box spectra approach these thresholds and serve as finite-volume comparisons; no numerical fit enters the continuum result.

With current advances in gravitational wave (GW) detection made by the worldwide LIGO-Virgo-KAGRA (LVK) network of detectors, ever-more sensitive tests of gravity in the strong-field regime are now possible. This enables one to test gauge theories beyond Einstein-Hilbert action, such as Weyl gauge theories of gravity. The only anomaly-free (quantum) gauge theory of a space-time symmetry beyond Poincaré is based on Weyl gauge group (of dilatations and Poincaré symmetry) with Weyl conformal geometry as its natural underlying geometry. This gauge theory has spontaneous breaking of Weyl gauge symmetry to Einstein-Hilbert and Proca actions, plus a positive cosmological constant. We investigate the GW polarisation modes of Weyl (quadratic) gauge theory of gravity in Weyl geometry and compare our findings to the most recent experimental data. We show how the geodesic deviation equation from Riemannian geometry translates to Weyl geometry, and explain why it is crucial to perform the analysis around de Sitter background, which is the correct low-energy limit of Weyl quadratic gravity, to not alter the GW content, and then compute the polarisation modes. In addition to the two transverse-traceless tensor modes predicted by Einstein-Hilbert action, we find two additional vector modes induced by the transverse fluctuations of the Weyl gauge field. If detected, these vectors modes would be important evidence for Weyl gauge symmetry.

Self-interacting dark matter turns the structure of galactic halos into a direct requirement on a low-energy scattering amplitude. We show that, for weakly coupled scalar dark matter, this requirement implies a much stronger mass bound on the dark matter particle than partial-wave unitarity alone. Using analyticity, crossing symmetry, locality and partial-wave unitarity, we compute the maximal allowed threshold amplitude with a dispersive primal S-matrix bootstrap, assuming only a weakly coupled EFT below a scale $\Lambda$ and allowing arbitrary UV particle content above $\Lambda$. For the benchmark self-interaction cross section $\sigma_{\rm self}=10^{-24}(M/\mathrm{GeV})\mathrm{cm}^2$, the mass of a generic weakly coupled scalar satisfies $M\lesssim 0.3\,\mathrm{GeV}$ in the controlled EFT regime. If dark matter is a derivative-dominated pseudo-Nambu-Goldstone boson, the mass bound is lowered to the MeV scale or below, depending on the hierarchy $M/\Lambda$.

We investigate the trans-series structure of the cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory and the dynamically generated mass gap of the $\mathrm{O}(6)$ sigma model at strong 't Hooft coupling. We consider the one-parameter deformation of the cusp anomalous dimension, known as the tilted cusp, and review its strong-coupling expansion obtained through its representation in terms of Fredholm determinants with a matrix Bessel kernel. The advantage of this deformation is that the non-perturbative scales separate naturally, revealing structures that remain hidden in the physical limit. Motivated by this observation, we introduce the tilted mass gap, which reduces to the physical $\mathrm{O}(6)$ mass gap at a special value of the deformation parameter and exhibits a deep connection with the tilted cusp. This formulation allows us to determine the complete strong-coupling trans-series and resurgence structure of the $\mathrm{O}(6)$ mass gap, while extending and proving conjectured relations between successive non-perturbative corrections. Building on the underlying Fredholm determinant representation, we construct an Alien calculus that generates all non-perturbative sectors of these AdS/CFT observables directly from their perturbative expansions. Finally, we derive an exact all-orders relation between the strong-coupling trans-series of the $\mathrm{O}(6)$ mass gap and the cusp anomalous dimension of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory.