Papers

The reverse isoperimetric conjecture states that, at fixed thermodynamic volume, Schwarzschild–AdS black holes maximize entropy. We show that its local fixed-volume form admits a boundary-completed canonical-energy interpretation. The key observation is that the bulk Hollands–Wald canonical energy vanishes on exact stationary black-hole families, while the fixed-volume entropy Hessian is encoded in an asymptotic boundary contribution. The same structure governs the global comparison. We choose an affine parameterization of a fixed-volume stationary branch connecting Schwarzschild–AdS to the solution of interest. If the stationary boundary Hessian is non-negative along this comparison, entropy concavity gives the reverse isoperimetric bound, while equality is determined by the directions along which the boundary Hessian vanishes. In Einstein gravity this reproduces the area–volume inequality on the stated comparison branches, and the formulation extends naturally to Wald entropy in higher-derivative theories.

We point out that the masses of the highly excited bound quark-antiquark states in QCD$_2$ in the infinite $N$ limit may be determined in the framework of a simple quantum-mechanical model with the potential $V(x) = \sigma |x|$. In the ultrarelativistic case, the masses follow the pattern $$ \mu_n^2 \ =\ \frac {g^2 N}{2\pi} n, $$ which coincides with the law derived by `t Hooft by solving the Bethe–Salpeter equation. In the nonrelativistic case, the energy levels follow the asymptotics $\epsilon_n = \mu_n - 2m = Cn^{2/3}$, where the constant $C$ can be determined by solving the `t Hooft equation or alternatively the nonrelativistic Schrödinger equation.

We provide a semi-analytic calculation of the first quantum corrections to the symmetron fifth force around a planar source with nonzero thickness. We find a suppression of the fifth force compared with the classical prediction within a Compton wavelength of the source, which is of order 10% in the parameter region relevant to experiments like CANNEX, while the fifth force is enhanced at larger distances from the source. The resulting change in the spatial profile of the fifth force may be relevant to current and near future terrestrial and astrophysical tests of force laws, and has implications for the optimisation of experimental geometries, including atom interferometers. This work provides a key benchmark for future numerical studies of quantum-corrected fifth forces in screened scalar-tensor theories of gravity.

CIPro is a Mathematica package for constructing and analyzing complete intersections in products of projective spaces and line bundles over such varieties. It computes properties of complete intersections, such as Chern classes, Hilbert series, GV invariants and symmetries, as well as properties of line bundles on complete intersections, including their cohomology groups. The package also consolidates a number of data sets available in the literature into a single system, including the lists of complete intersection Calabi-Yau three- and four-folds. This short tutorial introduces the package, provides a brief discussion of some of the mathematical background underlying its computations, and gives a series of examples to illustrate its use. These tools are of utility for many computations in string compactifications, especially for Calabi-Yau geometries appearing in Heterotic and Type II constructions. Many tools apply beyond the Calabi-Yau context, including for example, almost Fano bases in F-theory.

We compute the amplitude for the scattering of a gravitational wave off of a spinless point particle at fourth order in Newton's constant, using the worldline quantum field theory formalism. A decomposition of our master integrals incorporating Murua coefficients allows us to entirely bypass the cut subtraction needed to convert the scattering amplitude into the Magnusian, the latter mapping directly onto the scattering phase shift in partial wave space. Elliptic functions appear in momentum space for the first time for this process at this order. To compare to the phase shift from black hole perturbation theory, we present an analytical method for performing the partial wave projection of the new elliptic sector to any partial wave order $\ell$, and verify the equivalence of the Magnusian and the phase shift. This demonstrates that point-particle worldline quantum field theory accurately describes Schwarzschild black holes up to $\mathcal{O}(G^4)$.

I formulate unresolved soft-photon sector of QED as open quantum system. Resolved charged particles and hard photons form the system, unresolved soft photons form the environment, and basic object is the reduced density matrix. A resolved outcome $f$ of multiple hard particles and photons has probability $P_{f}(i) =\sum_n|\langle f,n|S|i,0\rangle|^2=\langle i|F_f|i\rangle$, with Kraus operators $K_n= {}_{\rm soft} \langle n|S|0 \rangle_{\rm soft}$ and effect $F_f=\sum_nK_n^\dagger\Pi_fK_n$. The SK formulation places unresolved virtual and real terms in one doubled-contour expansion. At one loop they carry the same on-shell eikonal kernel with opposite signs. This elegantly organizes the QED probability: for the same observable, perturbative order, diagrams, and phase space, the OQS gives the same infrared-finite terms as the full-QED. The soft-photon evolution is a unitary coherent-state displacement driven by the scattering current. The equal-history identity of influence functional exactly normalizes this soft evolution; together with the soft-photon theorem it removes the IR divergent leading-soft factor from inclusive probability. I also derive explicit leading-soft QED realization of scale-parametrized Lindblad evolution on a fixed hard-branch space. Tracing an infinitesimal soft-photon shell produces diagonal jump operators whose entries are fixed by the corresponding eikonal emission amplitudes. The finite-shell map is a completely positive unital Schur channel and, in the sharp scale-invariant leading-soft regime, a dephasing semigroup of a completely-positive-divisible scale flow. The resulting logarithmic visibility slope and monotonic purity loss are off-diagonal predictions of the reduced-state description. The same controlled-displacement dilation gives the Sudakov probability, Poisson soft-photon multiplicities, and the bremsstrahlung number spectrum.

We establish a correspondence between the free-field construction and the minimal-model construction of the Calabi–Yau sector of the four-dimensional heterotic string compactified on Berglund–Hübsch type Calabi–Yau manifolds and their orbifolds. For Fermat-type polynomials the Calabi–Yau vertex operators expressed in terms of free fields are shown to correspond to products of primary fields of $\mathcal{N}{=}2$ minimal models. Using this correspondence we verify modular invariance of the free-field construction and extend it to Berglund–Hübsch Calabi–Yau orbifolds, deriving the conditions on complete vertex operators that parallel those of the minimal-model construction.

Extreme mass-ratio inspirals (EMRIs) are among the most promising sources for future space-based gravitational wave (GW) observatories and provide sensitive probes of additional fundamental fields in the strong-gravity regime. In the present work, we investigate eccentric equatorial EMRIs around Kerr black holes in the presence of a massive scalar field. We assume that the inspiralling object carries a scalar charge, therefore, emits scalar radiation in addition to GWs. By solving the massive scalar perturbation equation in the frequency domain, we compute the relativistic scalar energy fluxes at the event horizon and at infinity and incorporate them into an adiabatic inspiral model. We investigate the impact of the scalar charge and scalar field mass on the orbital evolution and gravitational waveforms by analysing the accumulated phase differences and waveform mismatches relative to both general relativity (GR) and the massless scalar limit. Our results show that the massive scalar radiation can produce significant GW dephasing, with the effect becoming increasingly pronounced for more eccentric orbits. In addition, the scalar flux is suppressed for larger scalar field masses as fewer scalar harmonics satisfy the propagation condition at infinity. Finally, using both Fisher-information-matrix forecasts and Bayesian parameter estimation, we assess the capability of the Laser Interferometer Space Antenna to constrain the scalar charge and scalar field mass. The two inference approaches gives consistent constraints, demonstrating that eccentric EMRIs provide a promising avenue for probing massive scalar fields and scalar-tensor extensions of gravity in the strong-field regime.

Because massive particles asymptote to timelike rather than null infinity, current flat space holographic proposals such as celestial or Carrollian holography struggle to describe scattering processes with massive external states. We take a step toward addressing this limitation by studying how information about massive scattering amplitudes is carried to the late-time limit of null infinity by soft graviton radiation. We show that continuity between the boundaries of timelike and null infinity implies that the late-time limit of the Bondi mass aspect naturally acts as a detector operator for massive outgoing radiation. We further relate in-in correlation functions of the Bondi mass aspect at $\mathscr{I}^+_+$ to weighted sums of scattering cross sections, implying that an observer at $\mathscr{I}$ can extract information about massive scattering processes at late times. Finally, we interpret the Bondi mass aspect as a Carrollian stress-tensor component, and study Ward identities to constrain its two-point functions.

In a Lorentz symmetric non-Hermitian (NH) Dirac theory, containing the canonical relativistic Hamiltonian accompanied by a masslike anti-Hermitian Dirac operator, when the associated NH parameter becomes spatially modulated it couples massless Dirac fermions as NH gauge fields. With specific choices of such resulting NH gauge potential, the system experiences NH magnetic fields. When a planar Dirac system encloses a finite flux of such NH magnetic fields, a manifold of spatially localized right or left zero-energy eigenmodes appear in the spectrum, which we numerically anchor from microscopic realizations of NH magnetic fields on graphene's honeycomb lattice. Potential experimental platforms to test these predictions are discussed. Altogether, zero-energy NH flat bands of right or left modes promise fascinating future realizations of NH magnetic catalysis, strongly-coupled NH fractional topological phases, and NH chiral anomaly, to name a few.

I propose a Hermitian extension of the Lorentz-symmetric Dirac theory by complementing the associated Hamiltonian with another masslike anticommuting Dirac operator. The resulting theory manifests the iconic linear energy-momentum relationship in any dimension ($d$) and hence the emergent nodal quasiparticle excitations are named hidden-ordered Dirac fermions, which are symmetry protected and their responses are analogous to those in original Dirac systems, however, in terms of a renormalized (due to the hidden ordering) Fermi velocity. Typically, such a hidden ordering pushes any quantum phase transition into an insulation toward even stronger coupling in any $d>1$. However, depending on the internal algebra between the candidate insulating order parameter and masslike Dirac operator, the hidden-ordering may survive or disappear near the corresponding itinerant quantum critical point. I construct lattice models for such hidden-ordered massless Dirac fermions and outline promising platforms (numerical and experimental) to test these predictions.

Investigating the non-perturbative behavior of QCD and the dynamics of strong interaction is crucial for the study of heavy quarkonia and the understanding of exotic fully-heavy tetraquarks. In this work, using the analytical exact iteration method (AEIM), the analytical eigenvalue solutions of the non-relativistic Schrödinger equation are obtained in the presence of topological defects and external magnetic flux. The interactions are modelled using a modified Cornell potential supplemented by harmonic and inverse quadratic terms. We demonstrate that the energy levels are distinctly shifted by the topological defect parameter ($\alpha$). The mass spectra of heavy quarkonia ($c\bar{c}$ and $b\bar{b}$) and fully-heavy tetraquarks ($cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$) across several radial and orbital excitation states are successfully calculated using this approach. The computed masses of bottomonium and charmonium accord well with current theoretical predictions and experimental findings. Our findings for the heavy tetraquarks are in line with previous theoretical investigations that consider tetraquarks as configurations of diquarks and antidiquarks. The numerical results demonstrate that a nontrivial interaction between the confining potential and the background space-time geometry governs the mass hierarchy of these exotic hadronic states, providing high-precision data with excellent agreement with established theoretical models and experimental benchmarks.

We develop a geometric interpretation of Schwinger–Dyson identities by showing that their violations are controlled by a single score-mismatch field $\delta s$. For an arbitrary sampled probability distribution $Q$ and equilibrium measure $P_{\rm eq}$, every Schwinger–Dyson violation is determined by $\delta s = \nabla \log (Q / P_{\rm eq})$, which characterizes the departure from equilibrium. Each Schwinger–Dyson identity measures a projection of this field onto a probe direction in configuration space. The relative Fisher information is its squared norm. This gives a universal bound relating Fisher information to the complete Schwinger–Dyson hierarchy, thus implying that convergence in Fisher information restores all Schwinger–Dyson identities. We further obtain a variational characterization of the relative Fisher information in terms of Schwinger–Dyson violations, leading to a natural tomographic interpretation in which increasingly rich families of probe fields encode progressively more information about the underlying probability distortion. The configurational temperature, within this framework, emerges as a distinguished Schwinger–Dyson probe. The Stein operators and score-function methods arise naturally from the same probability-geometric structure. The score-mismatch field, therefore, provides a unified geometric language for understanding Schwinger–Dyson identities, configurational temperature, Fisher information, and non-equilibrium sampling in stochastic processes.

We give an operadic approach to deformation quantization of vertex Poisson algebras, a chiral analogue of the traditional problem of deformation quantization of Poisson algebras. Our main result is an order-by-order deformation-obstruction theory for such quantizations, controlled by the chiral analogue of Poisson cohomology. In the special case of chiral quantizations of affine symplectic varieties, quantizations of the vertex Poisson algebras of functions on their arc spaces, we prove that this deformation-obstruction theory is controlled by their de Rham cohomology. As another application, we prove that the boundary Virasoro minimal models are rigid under deformations.

Supergravity solutions describing stacks of D$p$-branes with $p\neq 3$ feature a non-constant dilaton profile, which is holographically mapped to the running of the SYM coupling in $(p+1)$ dimensions. For D-instantons ($p=-1$), the lack of space and time in the IKKT matrix model makes such an interpretation difficult at first. In this letter, we propose a method to achieve this based on two closely related concepts: the IKKT method of integrating out heavy strings in a Coulomb branch vacuum and the matrix RG flow of Brézin and Zinn-Justin (BZJ). The notable difference between the two is that the BZJ RG flow also integrates over the Coulomb branch position. We first apply the Coulomb branch method and by relating the coefficient of the leading correction to the IKKT action with the string coupling, we can compute its dependence on the Coulomb branch position, finding a match between matrix theory and supergravity. Next, we apply the BZJ-flow to the IKKT partition function, which leads to a running of the coupling constant $g$ with the rank $N$ of the matrix model, reproducing the $N$-dependence of the axio-dilaton field in supergravity.

We develop a new approach to cosmological correlators, built on a simple physical fact: deep inside the Hubble radius every mode oscillates as a flat-space plane wave, the curvature of spacetime making itself felt only as the mode is stretched towards the horizon. A Laplace transform turns this observation into a computational tool, resolving each curved-space mode function into a continuous superposition of plane waves labelled by a dual variable and dressed by a kernel that encodes the spacetime geometry, field content and dynamics. Every time integral then reduces to an elementary flat-space one, yielding simple diagrammatic rules for cosmological correlators. We illustrate the construction on the massive single-exchange correlator. The Laplace representation makes its total- and partial-energy singularities transparent ”from flat space”, and yields a single closed-form, rapidly convergent series valid throughout the entire kinematic domain. Although developed for conformally coupled fields exchanging massive scalars in de Sitter, the approach carries over essentially unchanged to virtually all situations of interest in primordial cosmology.

Deep inside the horizon, every cosmological mode oscillates as a flat-space plane wave. A Laplace transform turns this fact into a general method: it resolves each curved-space mode into a superposition of plane waves dressed by a kernel that encodes the spacetime geometry, field content and dynamics, collapsing the time integrals onto flat-space ones. This provides simple diagrammatic rules that turn cosmological correlator diagrams into their flat-space counterparts integrated against Laplace-space kernels. On the paradigmatic massive single exchange, this integral representation makes the energy singularities manifest and evaluates in closed form as a single, rapidly convergent series valid throughout the kinematic domain, with no patching of separate expansions. The Laplace approach sheds conceptual and computational light on cosmological correlators in virtually any theory of the early universe.

A recurring universality appears in the low-temperature quantum thermodynamics of near-extremal black holes, where distinct parent geometries often lead to the same logarithmic temperature dependence at one loop. In this work, we study the Lichnerowicz spectral origin of this infrared universality and understand why the relevant spectral data become insensitive to the details of the parent geometry. For extremal near-horizon geometries containing a two-dimensional maximally symmetric throat, we construct the normalizable transverse-traceless tensor zero modes associated with near-horizon reparametrizations. Turning on a small temperature lifts these zero modes through the first-order deformation of the Lichnerowicz operator. Although the local matrix element depends on detailed parent-geometry data, these data cancel after projection onto normalized tensor modes, leaving the universal result. For static spherically symmetric backgrounds, the resulting eigenvalue shift is proportional to the Fourier mode number and temperature. For rotating backgrounds, the same structure persists in the near-horizon reparametrization tensor sector, while angular warp factors only modify the overall projection factor. We fix the normalized coefficient explicitly, showing how radial integration and bulk normalization remove the near-horizon Taylor coefficients. We further show that this lifted bulk spectrum is the Lichnerowicz realization of the Schwarzian soft sector. Thus, the universal one-loop temperature dependence in the tensor sector is traced to an infrared bulk-boundary matching between near-horizon tensor zero modes and boundary reparametrization dynamics.

The SO(1,3)-symmetric reduction of Yang-Mills theory on Minkowski space yields a stress-energy tensor that is smooth on the timelike and spacelike Lorentz orbits but diverges on the lightcone that separates the two regions. We ask what consistent source this singularity represents. A natural cure is a real shift of the singular denominator. This does not regularize the source but instead moves the singular support onto a hyperboloid off the cone, where the corresponding source cannot remain both conserved and traceless. Our analysis shows that the displaced support cannot retain both properties, whereas a completion on the lightcone can. The matching condition fixes this completion up to one parameter $\chi$, which has a causal interpretation as the relative weight of the future and past cones. On regular constant-time slices, the completed source carries zero total four-momentum, so its physical content is a residual causal charge inferred from its curvature response.

Recently, it was proposed that the leading high-energy behavior of scattering amplitudes is universal, independent of charge, thereby extending the equivalence principle beyond the graviton pole. In this Letter, we derive a sharper causality constraint on such behavior by studying the Regge limit of colored scattering. Parameterizing a trajectory by $s^{\alpha(t)}$ with $\alpha(0)=2-\delta$, we analyze the Shapiro/Wigner–Smith time-delays in the irreducible scattering channels. We show that any non-singlet trajectory with $\delta< 1/2$ produces a growing sign-indefinite time-delay (with $\delta=1/2$ a marginal, dimension-dependent case), which becomes dominant in the Regge diffusion region in the weak-gravity regime. The essential point is that, while the eikonal phase is naturally organized in $t$-channel irreducible representations, the physical time-delays are its eigenvalues in the $s$-channel. A non-singlet exchange therefore recouples into the physical channels with both signs, inevitably producing a negative time-delay in at least one channel.

We study the gauge invariance of different continuum methods to include non-perturbative effects in gauge theories. We work with three dimensional quantum electrodynamics and implement vertices using two different methods: a set of coupled Schwinger-Dyson (SD) integral equations, and the self-consistent equations obtained from the 3-particle irreducible (3PI) effective action. We work in Landau gauge and assess the extent to which results are gauge invariant by checking how well the Ward identity is satisfied. Our results show that there is a fairly significant violation of the Ward identity at large coupling, although the 3PI effective theory is slightly better than the SD vertex. We also compare the results of both calculations with the commonly used Ball-Chiu ansatz and show that the agreement of the ansatz with both non-perturbative vertices is fairly good at small coupling but deviates more significantly at large coupling. We compare results for the two point functions of the theory and discuss the possible implications for phase transitions.

The Hubble tension remains one of the most significant unresolved problems in modern cosmology. A key question is whether it may arise from underestimated systematic uncertainties in the different measurement techniques. In this context, new independent methods are of exceptional importance. We therefore pursue a novel approach to determining the Hubble constant, $H_{0}$ based on continuum time delay and spectral energy distribution (SED) modeling in active galactic nuclei (AGNs). Unlike conventional techniques, this method is entirely independent of the cosmic distance ladder and does not require cross-calibration against other distance indicators. As a result, it enables a direct determination of $H_{0}$, free from the arbitrary normalizations that often affect indirect measurements. We conducted a dedicated monitoring campaign of the Seyfert galaxy Fairall 9 and further developed the H0RIZON-AGN model to interpret the resulting observations. The model incorporates the effects of radiation reprocessing in the surrounding cold accretion disk, enabling a more realistic description of the observed continuum delays. Through the simultaneous modeling of the continuum lag-spectrum and the broadband SED of Fairall 9, we derived a Hubble constant of $H_{0}=72.4_{-3.7}^{+3.4} \, \rm km \, s^{-1} \, Mpc^{-1}$. Achieving a measurement precision of approximately 5% from a single source demonstrates the considerable potential of this method for independent determinations of the Hubble constant. Our determination of $H_{0}$ is broadly consistent, within the current uncertainties, with both early- and late-Universe measurements. Future applications of the method to larger datasets, particularly those provided by the Vera Rubin Observatory, are expected to reduce the uncertainty to below 1%, thereby establishing this approach as a powerful independent probe of the Hubble tension.

We present two novel approaches for the numerical evaluation of Feynman integrals based on their universal analytic properties related to positivity, namely complete monotonicity (CM) and Stieltjes properties. Building on recent results, we exploit the fact that scalar Feynman integrals in the Euclidean region are completely monotonic functions, meaning that all their derivatives have a fixed sign. Building on this observation, the CM bootstrap allows one to reconstruct integrals from differential equations without explicit boundary data, yielding rigorous bounds. The second method is based on a refinement of CM. We prove that Feynman integrals, within a certain range of parameters, are not only CM but in fact Stieltjes functions. This enables the use of Padé approximants with provable convergence properties in the cut complex plane, providing an efficient method for analytic continuation and fast numerical evaluation. We illustrate the method with simple examples such as the massive bubble integral and discuss applications to multi-loop integrals, including the 20-loop banana integral. Finally, we comment on a number of extensions of these novel avenues for computing Feynman integrals.

Boruch, Emparan, Iliesiu, and Murthy recently discussed index saddles for 5d black strings, showing that the black string saddle admits a decoupling limit to a complex, finite-temperature BTZ \times S^2 saddle that computes the index of the dual CFT. In this paper, we pursue an analogous construction for the D1-D5-P black string. We construct a four-charge index saddle in the four-dimensional STU model as the BPS limit of the non-extremal four-charge black hole, and show that it exhibits the new form of attraction. We then uplift it successively to five and six dimensions, via the 4D-5D connection and a chain of string dualities, to obtain the gravitational index saddle for the D1-D5-P black string. We take a systematic decoupling limit of this index saddle and obtain the BTZ \times S^3 saddle that computes the index of the D1-D5 CFT.

Biadjoint scalar theory has been widely studied, due to its being closely related to the double copy correspondence linking gauge, gravity and related theories. In this paper, we continue a programme of work in elucidating non-linear solutions of this theory, and find a family of new solutions that are richer and more complex than previous cases. Using an ansatz that can be embedded in any choice of non-abelian colour groups, we demonstrate the existence of non-topological solitons, whose existence is protected by carrying a U(1) charge associated with certain rotations in colour space. The solutions are time-dependent, and closely related to the well-known Q-ball solutions in other scalar field theories. We also show explicitly that our solution set contains those that are stable under small perturbations within a consistent truncation of the theory, and have finite energy in addition to being localised.

The double copy of form factors has revealed a striking feature: poles that are spurious from the gauge-theory perspective become physical propagators in gravity. At the same time, form factors obey hidden factorization relations on the kinematics of these poles. We explain both phenomena by introducing a dyeing procedure, which promotes the color-singlet operator, or the Higgs particle representing it, to an adjoint massive state. The original form factor is recovered by the inverse bleaching operation, realized as a $U(1)$ decoupling of the dyed leg. In the dyed theory, these apparent spurious poles turn into ordinary physical propagators of colored amplitudes, and the hidden factorization relations follow from standard BCJ relations. Applying this framework to multiple operator insertions gives a systematic double-copy construction for multi-Higgs amplitudes and, as a byproduct, reveals scalar-ordering sectors. We also discuss higher-length scalar operators and fermionic operators, including the dyed vector construction for $\bar{\psi}\gamma^{\mu}\psi$, as well as a loop-level example.

We consider the sum of the adjoint Reidemeister torsions and prove the integrality for twist knots and the meridian. We also give some concrete examples of the generating functions for these sums.

Computing Ricci-flat metrics on Calabi-Yau manifolds is challenging since no closed-form solutions are known. However, these computations are needed in order to make physical predictions in heterotic string theory, such as the masses of quarks and Yukawa couplings. In this manuscript, we present an overview of relevant literature for learning about Calabi-Yau manifolds, as ML researchers often face a steep learning curve when entering the field. Furthermore, we survey the impact of the manifold's symmetries on machine learning approximations to these flat metrics. We also characterise the isometries of Ricci-flat metrics, a result frequently omitted or used without proof. Then, we address symmetry breaking in point sampling and introduce a novel formula for computing volume ratios on general CICY manifolds. We conclude by presenting a new symmetry-aware model built using graph neural networks that avoids pathological behaviour witnessed in some other models.

We use a primordial Majorana field as a fermionic probe of quantum correlations during inflation. Working in a torsion-free FLRW spacetime, we derive the two-component Majorana mode equations in an axion-inflation background and construct the corresponding quadratic Hamiltonian in the paired momentum basis. Hamiltonian diagonalization and the fermionic squeezing formalism are shown to give the same Bogoliubov transformation, providing a direct map from the Majorana mode functions to the instantaneous occupation number and to the two-mode state of each $(\boldsymbol{k},-\boldsymbol{k})$ pair. Because Fermi statistics restricts each helicity sector to the vacuum and one-pair states, the resulting Hilbert space is finite and the bipartite quantum-information measures can be evaluated explicitly. We compute the von Neumann entropy of the reduced mode and the logarithmic negativity of the Majorana pair. Both diagnostics indicate that sufficiently light Majorana modes can retain enhanced super-horizon bipartite quantumness, with the logarithmic negativity making the residual inseparability especially explicit. Our result does not by itself constitute an observational Bell test or a complete decoherence analysis; rather, it identifies a Pauli-bounded matter sector in which horizon exit alone is not sufficient to erase the quantum signature encoded in the two-mode state, thereby motivating an open-system study of how reheating and inflaton-induced interactions classicalize primordial fermionic probes.

Under assumptions compatible with generic gravitational scattering, the vacuum relativistic gravitational field is entirely determined at leading order in the large radius expansion at spatial infinity by its supermomentum, its dual supermomentum and its global supertranslation frame. At subleading order, the gravitational field is determined by three additional sets of charges: the super-Lorentz charges, the leading mixed tail/ peeling-breaking charges and the leading peeling-breaking charges. In this work we provide a proper-supertranslation-invariant definition of these charges in terms of asymptotic Bondi-Sachs fields as well as a corresponding proper supertranslation and logarithmic translation invariant definition of these charges in terms of Beig-Schmidt fields. Using the properties of homogeneous and inhomogeneous solutions to relevant wave equations over the boundary de Sitter spacetime at spatial infinity, we derive the conservation law of super-Lorentz charges between the future and past of spatial infinity. We obtain that the super-Lorentz aspects are non-locally defined from the Bondi-Sachs fields.