Papers

We present CHESS (CHEbyshev pSeudo Spectrum), a Wolfram Language package for high-precision one-dimensional transport of {\epsilon}-factorized differential equations for Feynman master integrals. The solver works with the matrix obtained by pulling a differential one-form to a chosen path. This matrix may be supplied directly, or assembled from constant matrices and precomputed scalar pullbacks of the one-forms. The program combines Chebyshev-Lobatto spectral collocation, sparse matrix assembly, sequential propagation in the {\epsilon}-expansion, and residue-based regularization of spurious regular singular endpoints. Benchmarks for large multi-scale integral families show rapid node convergence and agreement with independent reference data where such data are available. In the fixed local-series comparison used here, the Chebyshev transports also give shorter wall times; the reported process-tree memory usage is comparable for the smaller parallel runs and lower for the largest benchmark system in that comparison.

Triangulations, i.e., well-structured decompositions of geometric objects into triangle-like pieces, are central objects in many domains of mathematics and physics. In particular, fine, regular, and star triangulations (FRSTs) of 4D reflexive polytopes give rise to smooth Calabi-Yau threefolds, which are of significant interest in string theory. However, the high dimensionality and combinatorial complexity of triangulations make them particularly challenging to model with classical numerical methods or machine learning. In this work, we show that transformers, equipped with an appropriate encoding scheme, can be effectively trained to representatively generate new FRSTs across a range of polytope sizes. Moreover, these models can also self-improve through retraining on their own output. This opens the door to both concrete applications to the classification of Calabi-Yau manifolds and further research in physics, combinatorics and algebraic geometry.

We show that there is an explicit resurgent duality between weak and strong coupling expansions when one of the expansions has zero radius of convergence and the other has infinite radius of convergence. This complements the situation where the convergent expansion has finite radius of convergence, or when both expansions have zero radius of convergence. We illustrate this phenomenon for the Airy and Pearcey catastrophe integrals, and we apply it to two physical examples: the weak and strong coupling expansions of Dyson-Schwinger equations in zero-dimensional scalar $\phi^4$ theories, and the short and long time expansions of the heat kernel trace for the fluctuation operator of the kink-antikink crystal saddle configuration in the Gross-Neveu model.

We compute the leading-order $1/N$ corrections to the central charges $C_J$ and $C_T$ in the conformal QED$_d$-Gross-Neveu-Yukawa (GNY) model and the scalar QED$_d$ in $d$ dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are obtained to order $O(1/N)$ for general $d$. In $d=3$, the $U(1)$ Abelian gauge theory possesses a topological $U(1)$ global symmetry, and we evaluate the central charge $C_J^{\text{top}}$ of the topological symmetry current to subleading order in the $1/N$ expansion. Our interest in these theories is primarily motivated by their potential connection to the $SO(5)$ symmetric deconfined quantum critical point (DQCP). We compare the large $N$ results for the central charges $C_J$ and $C_T$ with the conformal data of the $SO(5)$ DQCP obtained from fuzzy sphere and conformal bootstrap. The large $N$ predictions of the QED$_3$-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the $SO(5)$ DQCP.

Many phenomenological calculations involving massless or unstable particles suffer from divergences as mediating particles go on-shell. One way to deal with these divergences is via the Kinoshita-Lee-Nauenberg (KLN) theorem, which guarantees that by summing over all physically-degenerate processes, the divergences cancel and inclusive observables remain finite. However, actually implementing this theorem in practice requires handling disconnected diagrams, ill-defined distributional objects, threshold behavior and subtle regulator dependence. In this work, we formulate practical prescriptions for dealing with some of these issues by studying the KLN cancellation in an illustrative model exhibiting a t-channel divergence. We demonstrate intricate cancellations across several regularization schemes, connect our results to the complex-analytic structure of the underlying amplitudes, and take steps towards constructing a finite, fixed-order, inclusive t-channel collider observable. This work highlights both the utility of the KLN theorem, and also the technical subtleties and open questions involved with applying it in practice.

We investigate holographically dual descriptions of $(2+1)$-dimensional s-wave and p-wave superconductors in the framework of regularized four-dimensional Einstein-Lovelock gravity theories, incorporating higher curvature corrections beyond the Gauss-Bonnet sector. We first implement the 4D regularization of Einstein-Lovelock gravity with finely tuned coupling constants to include corrections up to any $K$th order in curvature. The bulk geometry is constructed from exact black-brane solutions characterized by the fine-tuned Lovelock coupling $\alpha$ and the highest power of curvature in the Lagrangian K. We then analyze the condensation of scalar and vector operators dual to minimally coupled matter fields, focusing on two bulk-field mass prescriptions, which significantly affect the superconducting phase. Our results demonstrate that higher curvature terms significantly modify the phase structure of both s-wave and p-wave systems and enhance the sensitivity of the condensates and critical temperatures to the gravitational couplings. In both cases, the critical temperature generally increases with the maximal curvature order K, leading to higher-$T_c$ phases compared to Einstein gravity, particularly for negative $\alpha$. The coupling $\alpha$ effectively governs the strength of higher curvature interactions in the bulk: positive $\alpha$ suppresses condensation and lowers $T_c$, whereas negative $\alpha$ enhances superconducting order and promotes higher-$T_c$ phases relative to Einstein gravity. We further study the optical conductivity and find that both the gap frequency and the ratio $\omega_g/T_c$ exhibit a strong dependence on $\alpha$ and $K$, deviating from the universal Einstein-gravity result. Higher curvature effects enhance the superconducting gap scale. Notably, the p-wave system shows a stronger sensitivity to the mass-fixing prescription compared to the s-wave case.

The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to integrable Hamiltonians with local interactions involving multiple degrees of freedom. In this work we characterize both the continuous and discrete symmetries of these equations required to establish an equivalence class of solutions. We find that the set of such symmetries depends on the number of sites on which the equation is supported. In several cases there are more symmetries than the standard Yang-Baxter equation, thus placing heavy constraints on the number of inequivalent solutions and the associated integrable models. As an application we show how to restrict the generic $16\times16$ ansatz to the 30-dimensional subspace invariant under a chosen discrete symmetry subgroup. An explicit $16\times 16$ solution is also written down.

In this paper we construct duality-covariant worldvolume dynamics of particles and branes. We extend known actions and phase space formulations to include the hidden $E_8$ symmetry of 11D supergravity, analogous to the Ehlers symmetry of 4D gravity. Making the worldvolume theory manifestly duality-covariant requires the ancillary structure of $E_8$ exceptional field theory to be taken into account. For zero-branes, we propose an enlarged worldline model with a coadjoint orbit term to encode this. More generally, we propose worldvolume theories for arbitrary exotic branes in a way that generalises the known gauged sigma model of the Kaluza-Klein monopole. These are natural in the duality-covariant Hamiltonian formulation employed here. We discuss the case of zero-branes in eleven dimensions as an illustrative example.

We study long-range tensor response and its coupling to matter through sourced spectral equations on fixed spacetime. For a response with a positive spectral representation, the weight at zero is extracted by an infrared limit. At an isolated critical mode, this weight is determined by the propagation slope and the projection of the source onto the critical space. Deriving the kernel and source maps from the same equations allows the residue to be followed through channel elimination and finite approximation. For isolated stationary matter, conservation relates the leading source to the total energy, including interaction contributions. We obtain separate estimates for the potential and force tails under the stated spectral assumptions. Compact spectral examples give explicit endpoint derivatives and tensor overlaps. We also classify the null-shell measure of a covariant stress-tensor realisation. The results provide a criterion for long-range matter exchange, with its gravitational interpretation determined by the tensor structure, coupling and infrared consistency conditions.

Extended black hole thermodynamics highlights a sharp tension in the usual holographic dictionary: at fixed boundary conformal frame, changing the AdS radius changes both the central charge and the spatial volume of the CFT, so that the color and volume sectors of the first law becomes degenerate. We show that this degeneracy is naturally removed for quantum black holes in Karch–Randall double holography. The mechanism is intrinsically semiclassical. Replacing the holographic regulator surface by a physical brane induces gravity coupled to a cutoff CFT, so classical bulk black holes become lower-dimensional quantum black holes whose geometry includes the cutoff-matter stress tensor to all orders in backreaction. This backreacting matter sector supplies a color variable distinct from the defect volume. We demonstrate the mechanism explicitly for the quantum BTZ black hole. Thus quantum backreaction resolves the same color-volume degeneracy addressed by the recent Weyl-factor proposal, but without introducing a non-standard boundary Weyl factor. Instead, the missing thermodynamic direction is supplied by the physical cutoff-matter sector of the doubly holographic quantum black hole.

Arguments for emergent spacetime require that quantum typicality, the generic absence of inter-subsystem correlations, persists on the physical Hilbert space of a gauge theory, where non-Abelian constraints could in principle inject geometry-supporting entanglement. Using $SU(2)$ lattice gauge theory on two-dimensional tori ($d_{\mathrm{phys}}$ up to $4{,}193$), we show that it does: the typical mutual information between strictly disjoint links matches an exact parameter-free analytical prediction combining a microcanonical baseline with Haar-random fluctuations. The Kogut-Susskind Hamiltonian generates correlations from states of definite geometry (such as the electric vacuum), while generic states show only regression to the mean, establishing that the arrow of correlation growth requires a non-generic initial condition.

We investigate bipartite quantum correlations of Dirac fields in the spacetime of a Hayward regular black hole. Using the Wootters concurrence and the CHSH Bell parameter, we analyze the influence of Hawking radiation on an entangled state shared by an inertial observer and a near-horizon observer. We show that, unlike the bosonic case, fermionic correlations remain nonzero even in the infinite-temperature limit owing to the Pauli exclusion principle, while part of the entanglement is redistributed to inaccessible modes inside the horizon. The accessible modes exhibit Bell nonlocality for all finite Hawking temperatures, whereas the interior modes never violate Bell's inequality. The Hayward regularity parameter $g$ affects the correlations only through the Hawking temperature, whose decrease with increasing $g$ enhances the preservation of quantum information. These results suggest a close connection between singularity resolution and the robustness of fermionic quantum correlations in regular black-hole spacetimes.

We develop a unified thermodynamic description of dynamic thin-shell wormholes, starting from the transparent (vacuum bulk) case and then relaxing the transparency condition to include bulk matter crossing the throat. For isolated shells, we show that the entropy is conserved under transparent evolution, $TdS=0$, which holds for arbitrary dynamical motion of the throat within the assumptions of the thin-shell formalism. When bulk matter is present, the generalised first law becomes $T\dot{S}=A\Phi$, where $\Phi$ is the net energy flux; entropy increases (decreases) when matter flows into (out of) the shell. Explicit expressions for the flux are provided for null dust and massless scalar fields, and quantum pair production (Hawking-like emission) is also discussed. A formulation of the generalised second law is presented, and it is consistent with standard thermodynamic expectations under conditions where heat flows from hotter to colder regions. As a concrete astrophysical application, we study accretion of null dust: the critical accretion rate above which the throat becomes dynamically unstable depends sensitively on the spacetime geometry and the shell equation of state, highlighting the environmental dependence of these configurations. Fluctuations in the energy flux induce a stochastic force on the throat dynamics, leading to a Langevin description with an associated fluctuation-dissipation relation. This results in diffusion of the throat radius and additional entropy production. The framework applies to a broad class of spherically symmetric thin-shell constructions within general relativity. Our results provide evidence that thin-shell wormholes admit a consistent thermodynamic description, quantify their sensitivity to accretion processes, and suggest possible avenues for probing exotic compact objects with future gravitational wave observations.

We generalize the "holar wind" mechanism proposed in arXiv:2303.00234 to the case of rotating $\lambda$-deformed BTZ black holes. These backgrounds, which interpolate between $AdS_3$ in the infrared and a linear dilaton spacetime in the ultraviolet, are realized as an exact $\frac{SL(2,\mathbb{R})_k\times U(1)}{U(1)}$ gauged-WZW worldsheet theory. The long string sector of the theory provides a holographic dual to single-trace $T\overline{T}$ deformed symmetric product $\mathcal{M}^p/S_p$ $CFT_2$ with a seed $\mathcal{M}$ carrying a central charge $c=6k$. By analyzing the geodesics and tunneling rates of probe particles and winding long strings, we show that the emission probabilities for both positive and negative deformation couplings are universally governed by the change in the Bekenstein-Hawking entropy, $\Delta S_{BH}$. A central result of our analysis is that the consistency of long string emission within the grand canonical ensemble dictates a unique value for the background B-field at the origin. We demonstrate that this thermodynamically fixed value matches precisely the prediction required for the string excitation spectrum to agree with the $\mathbb{Z}_w$ twisted sector of a single-trace $T\overline{T}$ deformed symmetric product orbifold. Finally, we sketch the extension of these results to a broader class of black holes whose long string sector is dual to single-trace $T\overline{T} + J\overline{T} + T\overline{J}$ deformed theories.

We consider Yang–Mills, Chalmers–Siegel and self-dual Yang–Mills (SDYM) theories within AdS/CFT correspondence. Bulk-to-bulk and boundary-to-bulk propagators are derived in various gauges and for Dirichlet, Neumann, mixed and self-dual boundary conditions. Three- and four-point holographic correlators are computed in the three theories to establish the relation between the observables thereof. This is a companion paper to [arXiv:2602.21658].

We study the closed-string tachyon and doubled Ramond-Ramond sector of type 0A in light of the proposed M-theory description on $S^1\vee S^1$-the wedge of two circles joined at a point. In this picture the two RR copies are associated with the two circle components, which we call branches, and tachyon condensation corresponds to shrinking one branch to the type IIA endpoint. From the type 0A equations of motion, we derive the branch-balance condition for a tachyon stationary point and identify the branch-odd RR fluctuation that sources the tachyon around a symmetric background. We then analyze the fate of the collapsing branch RR data as one branch of the wedge collapses to the type IIA endpoint. For an isolated unscreened collapsing-branch $D_p^-$ source, a Gauss-law estimate shows that the long-range RR field-energy cost scales inversely with the shrinking circle and thus becoming infinitely costly, generalizing the $D0^-$-brane decoupling in the original wedge picture. We describe the infrared screening of the relative RR field through an effective higher-form Stückelberg mechanism and distinguish this from a possible discharge of localized relative charge. Finally, using standard Wess-Zumino couplings of D-branes, we identify an effective relative-charge carrier and derive a parametric thin-wall criterion for when such a discharge channel $D_p^- \to D_p^+$ can be energetically favored.

We present new charged and rotating near-horizon geometries in five-dimensional Einstein-Maxwell theory in closed analytic form. The solutions can be parametrised by the charge and two independent angular momenta. We also generalise these near-horizon geometries to theories with an additional Chern-Simons term in the action multiplied by an arbitrary coupling constant. The new solutions have the same entropy relations as expected for charged versions of extremal Myers-Perry black holes and for rotating versions of extremal Reissner-Nordström-Tangherlini black holes, but they do not reduce to the Myers-Perry horizon in the vacuum limit. The horizon cross-sections are spherical and carry a Sasakian structure. We exploit this structure to prove a characterisation of our solutions: without any symmetry assumptions, they are the most general rotating extremal horizons for which the co-rotating electric field is a (non-zero) constant. We further extend this construction to higher dimensions, where we show that any Sasaki-Einstein manifold generates a two-parameter family of charged and rotating horizons.

What is the density of states of the de Sitter static patch? We propose a definition and calculation of such a density in 3d dS. Our proposal involves a sum over an SL(2,$\mathbb{Z}$) set of Euclidean no-boundary Kerr-lens spacetimes sourced by a line-defect with given energy and spin - which in Lorentzian time represents an observer's worldline at the center of the dS static patch. We develop an exact quantum computation of the spectral density using a holographic duality between dS$_3$ gravity and two copies of $\mathbb{C}$LS, the complex Liouville string. The SL(2,$\mathbb{Z}$) Kerr-lens spacetimes map under the duality to an SL(2,$\mathbb{Z}$) family of generalized crosscap geometries. We compute the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS crosscap amplitudes and show that they match the semi-classical gravity prediction. For the simplest non-trivial Kerr-lens space, the $\mathbb{C}$LS $\otimes$ $\mathbb{C}$LS description is, in turn, dual to two copies of the $G\Sigma$ effective field theory of the double scaled SYK model. The $G\Sigma\otimes G\Sigma$ theory lives on an observer's worldline in the static patch, setting the stage for developing a microscopic worldline hologram of 3d de Sitter.

We present a field-level perturbative forward model for the Lyman-alpha (Lya) forest flux decrement. We validate it on two simulation suites: large-volume AbacusSummit N-body simulations with the Lya forest painted onto the dark matter field, and the Sherwood hydrodynamic simulations. Across the redshift range of the simulations (z=2.0-3.2), the 3D and 1D power spectra of the model match the simulated Lya fields at the 1% (5%) level up to k <= 0.3 (1.0) h/Mpc, with similar performance for the cross-correlation with massive dark matter halos. The counts-in-cells statistic shows excellent agreement down to cell radii of 2 Mpc/h. Leveraging cosmic variance cancellation, the model enables precision measurements of Lya bias parameters and robustly detects the full set of quadratic line-of-sight bias operators, consistent with the notion of naturalness in effective field theory (EFT). We quantify the stochasticity of the Lya forest (the analog to the one-halo term), and find it to be white (scale- and orientation-independent) on large scales, matching EFT predictions. We further find that phenomenological flux power spectrum models, based on modulations of the linear-theory power spectrum, fail at the field level even on quasi-linear scales. For the currently observing Dark Energy Spectroscopic Instrument (DESI), we generate large-scale clustering mocks of the Lya forest to validate cosmological parameter inference pipelines. Looking ahead to its successor, DESI-II, we produce large-volume mocks of representative samples of Lyman-break galaxies (LBGs) and Lya emitters (LAEs), calibrated on Astrid hydrodynamic simulations and matched to observations at z=3, enabling joint analyses of Lya forest and high-redshift galaxy data.

We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge $Q$. Using both a large-$N$ BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, $\chi\,\xi^{1/6}(24Q)^{1/9}\,\hbar\omega + \cdots$ where $\xi$ is the Bertsch parameter, and $\chi$ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same $Q$ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.

We give a formula for conserved charges in an arbitrary Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The formula is determined by the theory's $L_\infty$ data alone, without reference to the derivative structure of the Lagrangian. Therefore conserved charges can be computed in nonlocal models, such as string field theory, where conventional methods break down. The formula also gives the correct expression for the Hamiltonian of general relativity as a surface integral of the Brown-York stress tensor. Related computations in Yang-Mills theory suggest that spatial boundaries are dealt with in a natural fashion.

We review the representations of so(1,D), the algebra of isometries of D dimensional de Sitter space. We cover the representations in all D, including mixed symmetry representations and fermionic representations, and connect them to the various types of fields that can propagate on de Sitter space. The presentation is from a physics point of view, favoring concrete constructions over abstract considerations.

We investigate the extended thermodynamics, including the Joule-Thomson expansion and $P-V$ criticality, of a four-dimensional charged anti-de Sitter (AdS) black hole within the combined framework of ModMax nonlinear electrodynamics and dRGT-like massive gravity. Operating in the extended phase space and employing the generalised Sharma-Mittal entropy to account for non-extensive statistical correlations, we derive exact analytical expressions for the modified Hawking temperature, specific heat, Joule-Thomson coefficient, and the equation of state. Our analysis of the throttling process reveals that the conformal nonlinearities of the ModMax field ($\gamma$) expand the physically accessible cooling domain by shifting the inversion transition to smaller horizon radii. While the Sharma-Mittal parameters ($\delta$, $R$) critically govern local thermodynamic stability and the inversion radius, the global inversion phase boundary remains fundamentally dictated by the massive graviton background. Furthermore, an analysis of the Gibbs free energy uncovers a van der Waals-like first-order phase transition characterized by a distinct swallow-tail structure. We observe a clear physical decoupling in the critical regime: ModMax nonlinearities modify the critical phase boundary by suppressing electromagnetic interactions, Sharma-Mittal parameters dictate the relative thermal stability of competing phases, and massive gravity governs the overarching macroscopic phase landscape. These results highlight the sensitivity of thermodynamic phase phenomena as robust diagnostic tools for distinguishing nonlinear and non-extensive modifications to black hole physics.

We construct an exact solution for the electrically charged extension of a distorted black hole spacetime within Einstein-Maxwell theory using the Harrison transformation. The resulting solution represents a charged deformation of a static distorted vacuum geometry in which the electromagnetic field is introduced through a nonlinear transformation preserving the radial structure of the seed spacetime. Consequently, the Killing horizon remains determined solely by the seed metric and it is not shifted by the electric charge. We analyze the thermodynamic properties of the solution and show that the horizon area, entropy, and temperature are governed by the geometric sector, while the electric charge enlarges the thermodynamic phase space through the electromagnetic potential. The motion of charged test particles is studied using the effective potential formalism, where the distortion parameter modifies circular orbits and shifts the location of the innermost stable circular orbit. We also investigate the black hole shadow for a static observer at finite distance and show that the distortion parameter displaces the photon sphere outward, increasing the apparent shadow size. A geometric correspondence between the photon orbit, determining the shadow and the leading eikonal quasinormal-mode frequency, is discussed, linking optical and perturbative observables. Finally, we study charged scalar perturbations and show that the vanishing horizon electric potential prevents a charged superradiant amplification. In the weak-coupling regime, the quasinormal-mode spectrum is estimated using the WKB method, where the electromagnetic interaction enters through the gauge-invariant combination $(\omega - q_s \xi_t)$ and shifts the oscillation frequencies of the perturbations.

Horizon-scale imaging acts as a transformative tool for probing spacetime geometry, enabling stringent tests of gravitational theories in the strong-field regime. The Casadio-Fabbri-Mazzacurati(CFM) black hole in braneworld contains an extra parameter that characterizes the tidal effects from the bulk geometry, making it highly valuable for this task. We perform general relativistic radiative transfer (GRRT) simulations and generate synthetic images consistent with Event Horizon Telescope observations of M87*. We find that the tidal parameter imprints nonmonotonic changes on the image morphology, underscoring the intricate coupling between spacetime geometry and the observable radiation from the accreting plasma. We also analyze the image-comparison metric using normalized cross-correlation coefficients and the DSSIM index and find that the magnitudes of these mismatches are on the order of 10^3, which implies that identifying braneworld black holes through black hole images remains challenging even with future ngEHT and BHEX observations.

We develop the boundary large-rank interpretation of finite Carrollian black-hole thermodynamics and its sourced stress, scalar spectral and interacting thermal observables. Correlated scaling of the time generator and Newton coupling preserves the extended Hamiltonian differential while the generator temperature vanishes and the holographic normalization grows. The Brown–York source variation fixes the relative weights of energy density, momentum density and spatial stress, giving Ward equations on the Carrollian and thermal time scales. Boundary volume and normalization variations reproduce the bulk pressure work and characterize the Hawking–Page crossing through a chemical potential. Source coupling fixes the scalar operator map and spectral clock Jacobian. Numerical solutions in four-dimensional Schwarzschild-AdS determine angular transmission and finite-frequency absorption. In the type IIB family, the logarithmic scrambling interval imposes an additional hierarchy between rank and 't Hooft coupling. We derive a correlated limit in which the string length vanishes while a finite transverse Regge kernel survives in the normalized four-point functional. Its integrated attenuation and spatial width obey a common relation. This interacting observable distinguishes large-rank sequences with the same leading thermodynamics and asymptotic Regge growth rate. Thermal Fourier–Mellin moments retain the scalar spectrum in a contracting frequency window. Time translations shift their weights with angular source terms retained. The BTZ dictionary supplies the corresponding large-central-charge equilibrium example.

We study the symmetry structure of four-dimensional axiverse effective field theories with multiple axions coupled to abelian gauge sectors, including their extensions to broad classes of N=1 models. We identify the invertible and non-invertible generalized symmetries, and discuss the associated symmetry-breaking mechanisms together with the resulting hierarchies of energy scales. In particular, we discuss the quantum-gravitational breaking of non-invertible axion shift symmetries predicted by the existence of wormholes and the recently proposed Imaginary Distance Bound. In N=1 axiverses, these wormhole-based arguments imply that towers of BPS EFT instantons play a distinguished role and generate infinitely many superpotential terms.

Symmetry-protected low-scale seesaw models can account for the observed neutrino flavour oscillations without fine-tuning, while yielding collider-accessible signatures through pseudo-Dirac heavy neutral leptons (HNLs). Seesaw frameworks generically predict lepton number (LN) violation, which provides a powerful discovery channel. In symmetry-protected realisations, however, the amplitudes for LN violation are strongly suppressed by destructive interference between the contributions of the two quasi-degenerate HNLs within the usual QFT plane-wave treatment. We demonstrate that damped heavy neutrino-antineutrino oscillations significantly alleviate this suppression. We compare the sensitivities to pseudo-Dirac HNLs in both LN-blind and LN-violating channels at the LHC and future hadron colliders such as the FCC-$hh$ and the S$pp$C. We find that, although searches for LN violation outperform their LN-blind counterparts, small mass splittings in the pseudo-Dirac HNL pair can drastically reduce the sensitivities in these channels. We further show that combining LN-blind and LN-violating searches can distinguish a pseudo-Dirac HNL pair from the double-Majorana limit in the intermediate regime where LN violation is observable but not yet saturated.

This work develops a phase-based formulation of relativistic wave dynamics, demonstrating that the Klein–Gordon equation emerges naturally from the foundational assumption of intrinsic phase periodicity in material fields. Mapping the phase directly onto the classical action, we postulate that localized excitations possess an invariant rest-frame oscillation governed by a proper frequency $\omega_0$. This physical condition establishes an operational mass-frequency relation, $m = \hbar \omega_0 / c^2$, without requiring rest energy as an independent, axiomatic input. We show that the Klein–Gordon equation arises as the minimal local, linear, Lorentz-invariant field equation compatible with this internal phase structure. Within this framework, mass acts as an intrinsic frequency scale governing wave propagation, and relativistic kinematics is fully recovered as a structural consequence of phase coherence. This approach provides a unified wave-mechanical interpretation where particle dynamics maps onto the group velocity of dispersive wave packets, offering an intuitive account of free propagation, dispersion, and tunneling across potential barriers.

We present the mixed QCD-electroweak corrections to Higgs boson pair production in the quark-antiquark channel. The virtual amplitudes are computed fully analytically using the method of differential equations. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We implement the results in the POWHEG-BOX framework for phenomenological studies. The corrections are found to have a significant impact on the shapes of differential cross sections, reaching up to +10% for the invariant mass distribution of the Higgs boson pair near the production threshold. This channel has not been considered before in calculations of the next-to-leading order electroweak corrections to Higgs boson pair production.