Papers

In a Hamiltonian lattice gauge theory, the physical Hilbert space is fixed by the Gauss law, by choosing an eigenspace of the Gauss law operator which generates the gauge transformation. Choosing a non-trivial eigenspace is referred to as the modified Gauss law. In 2+1d dynamical U(1) pure gauge theory, we show that these physical Hilbert spaces are defect Hilbert spaces associated with non-topological monodromy defects for monopole operators and topological defects for U(1) 1-form symmetry, inserted along the time direction. We also construct the corresponding lattice translation operators. Under a nontrivially modified Gauss law, these translations obey a magnetic translation algebra. Finally, we discuss how the modified Gauss laws are manifested in 2+1d compact bosons, via exact duality on the lattice.

Massless particles, defined through Wigner's induced representations of the Poincaré group, are obtained as a limit of infinitely boosted massive particles wherein the massive little group undergoes an Inönü–Wigner contraction to the massless one. It is demonstrated that the spin-$s$ multiplet of a massive representation re-organizes into the direct sum of massless particles with helicities in the range $[-s,s]$. This group theoretic result is the Hilbert space counterpart of the Stückelberg formulation of massive fields of spin $s$ in the high-energy limit, where the Stückelberg fields become independent massless fields of spins $s'\leq s$ in integer steps. It therefore also provides the kinematic setting of the Goldstone equivalence theorem.

How does continuum operator structure appear in a finite qubit register? We address this question for analytic functions of diagonal operators represented in a binary basis, focusing on the Jordan–Lee–Preskill (JLP) momentum operator, by developing an operator-level generating-function framework for their Walsh-Pauli spectra. The construction determines the spectrum analytically and reveals exact support and parity selection rules, together with a nontrivial intra-shell hierarchy induced by the binary encoding. This provides a systematic characterization of Walsh compressibility and its relation to Pauli locality. As a controlled application, we consider generalized uncertainty-principle (GUP) kinematics as a tunable nonlinear odd deformation of momentum, showing how higher-order momentum terms redistribute spectral weight into progressively higher Pauli-weight sectors

We investigate whether dimensional deconstruction can qualitatively modify long-range forces. We show that the deconstruction of a five-dimensional AdS spacetime effectively generates an inverse-square potential, which naturally gives rise to broad p-wave Sommerfeld resonances without fine-tuning. We then apply this mechanism to dark matter phenomenology.

We revisit the role of the trace sector of the graviton in covariant string amplitudes by constructing the ghost-number-three graviton vertex operator via BRST descent, imposing only the de Donder gauge condition without requiring tracelessness. The resulting operator is well defined even at zero momentum, while for nonzero momentum the trace-dependent sector of the descent chain forms a trivial BRST descent chain. Evaluating its disk one-point function in the presence of a D$p$-brane, we show that the trace-dependent term is essential for reproducing the correct graviton-brane coupling, canceling the Dirichlet-direction contributions and leaving the expected coupling to the world-volume components.

We realize a nearly pure higgsino dark matter candidate with mass of about 1 TeV in the Minimal Supersymmetric Standard Model coupled to the Starobinsky supergravity. The recent LUX-ZEPLIN 248 keV nuclear-recoil event has renewed interest in higgsino dark matter. In this framework, the particle spectrum, including the Higgs boson mass, the higgsino mass and its splitting, is connected to cosmic inflation observables via gravitational mediation of supersymmetry breaking and subsequent renormalization group evolution. We show that the Higgs boson mass predicted by the model agrees with the measured value within the quoted uncertainties for a broad range of bino-induced mass splittings. Wino-induced splitting leads to a Higgs mass several GeV higher and is therefore excluded.

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.

The axion is a promising candidate for solving the strong CP problem. To solve this problem, the global U(1) symmetry must be preserved to a high degree of accuracy. However, it is well known that global symmetries are explicitly violated by quantum gravity effects, giving rise to what is referred to as the axion quality problem. In this paper, we investigate axionic wormholes as a source of explicit U(1) violation in Metric-Affine Gravity. This framework allows for spacetime torsion and non-metricity, which accommodate additional curvature-like and topological terms, such as the Holst and Nieh–Yan terms, that are absent from the metric and Palatini formalisms. We show that non-minimal couplings to these terms modify the wormhole dynamics and enhance the Euclidean wormhole action, thereby alleviating the axion quality problem. We also find that the viable parameter space is enlarged when two of these couplings are simultaneously present. We further identify representative parameter regions where the alleviation of the axion quality problem is compatible with inflationary constraints.

The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-\epsilon$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(\epsilon)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer Rényi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer Rényi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

The gravitational field of a physical cosmic string is regular on the axis, curved across a finite vortex core, and only asymptotically conical. We test whether the bound-state spectrum of a transverse Dirac oscillator resolves this structure beyond the ideal-cone approximation. The fermion is treated as a test field on self-consistent Einstein–Abelian-Higgs vortex backgrounds, and the radial problem is cast as a generalized Hermitian eigenvalue problem. The numerical formulation is checked against the exact Minkowski and ideal-cone spectra and by independent shooting calculations. For a reference vortex family, the finite-core correction grows from the weak-confinement regime toward the percent level. When the normalized asymptotic cone is held fixed, the spectrum still varies with the measured Higgs-core radius, and the sampled backgrounds bracket a change of sign of the ground-state correction. The bound-state spectrum therefore contains information about the resolved core profiles that is not fixed by the asymptotic cone alone.

We examine how $s$-channel unitarization changes the dynamical gluon mass scale $m_g$ inferred from high-energy elastic $pp$ scattering. The Born input is the Reggeized Landshoff–Nachtmann exchange of two nonperturbative gluons in a color-singlet state. We fit the ATLAS and TOTEM forward data separately, using eikonal and $U$-matrix unitarizations with logarithmic and power-law running masses derived from Schwinger–Dyson analyses. At the common reference cut $|t|_{\rm max}=0.12~\GeV^2$, the Born fits give $m_g=297$–$427~\MeV$; the eikonal and $U$-matrix fits give $265$–$360~\MeV$ and $243$–$328~\MeV$, respectively. Unitarization changes the fitted values of the intercept parameter $\epsilon$, $m_g$, and the exponential slope $a_1$ of the proton form factor together. Over $0.10\leq |t|_{\rm max}\leq0.14~\GeV^2$, the $U$-matrix parameters vary less with the cut, while the eikonal fits to TOTEM show a pronounced drift. Replacing the infrared continuation of the logarithmic effective charge by a Curci–Ferrari prescription changes $m_g$ by a mean absolute relative shift of $1.77\%$ over twenty comparisons, with a maximum of $2.17\%$. The inferred scale remains in the few-hundred-MeV region, but its fitted value depends on the nonperturbative input and on the unitarization prescription.

The AKSZ construction encodes the Batalin-Vilkovisky formulation of a topological field theory in terms of finite-dimensional geometric data. There are at least two ways to extend this approach to nontopological gauge theories. The first, due to Costello, replaces the spacetime exterior algebra with a more general DGCA that is not freely generated. The second replaces the symplectic structure with a degenerate presymplectic structure, which may also be non-regular. In this work, we show that both approaches are special cases of a more general algebraic AKSZ construction, in which the underlying algebras are allowed to be constrained and the presymplectic structure may be degenerate and non-regular. Within this framework, we explicitly relate Costello's formulation of the Chalmers-Siegel model to the presymplectic formulation, the latter admitting a first-principles derivation. We also construct Costello-like formulations of higher-form analogues of the Chalmers-Siegel model and of self-dual higher-spin gauge theories of Yang-Mills type, obtaining in the latter case a remarkably concise description. In so doing we propose a simple algebraic construction for the corresponding source space DGCAs underlying these examples.

We describe a large class of theories that continuously interpolate between single and double trace $T\bar T$ deformations of AdS$_3$/CFT$_2$. It is obtained by starting with the spacetime $M_3$, which interpolates between AdS$_3$ in the IR and a linear dilaton spacetime in the UV, and imposing a UV cutoff on the radial direction. When the cutoff is deep in the AdS$_3$ region of $M_3$, this leads to double trace $T\bar T$. When it goes to infinity, we recover the single trace deformed theory. We present a large class of possible boundary conditions on the dilaton, and compute the resulting black hole spectrum in a few examples. In all these constructions, to leading order in the low energy expansion, the resulting spectrum is that of a single $+$ double trace deformed CFT, but at higher orders the different theories have different spectra. In one of the examples that we analyze, the full theory is single $+$ double trace $T\bar T$ deformed CFT. Another gives rise to an interesting spectrum, that consists of an infinite set of energy bands.

We investigate the fate of asymptotic particle states in supersymmetric quantum field theories on de Sitter backgrounds, distinguishing algebraic field content from localized LSZ-like excitations. We study how long-wavelength gravitational fluctuations may suppress pole residues and redistribute spectral weight from isolated contributions toward continuum sectors. The analysis is formulated within a Kallen-Lehmann spectral framework and is intended as a structural infrared mechanism rather than a non-perturbative proof of de Sitter quantum gravity. The paper develops three connected levels. First, we analyze residue suppression in a quasi-de Sitter setting and its possible transmission through Yukawa and gravitational interactions. Second, we formulate the spectral decomposition as a map between the full field-theoretic spectrum and the observable particle sector. Third, we examine a conditional cosmological realization of redistributed spectral weight, including possible effects on expansion, structure growth, and lensing. This cosmological layer is a downstream phenomenological test and is not used as evidence that pole loss has occurred. In the current MCMC analysis we find S8 approximately 0.803 and, when the smooth fraction is varied, fS8 = 0.0025 +/- 0.0017, consistent with the benchmark value 0.00262. These results test the internal consistency of the proposed realization but do not establish the dark-sector assignment or the underlying infrared mechanism.

Anti-de Sitter (AdS) spacetimes are not globally hyperbolic, so boundary conditions are generally needed for well-defined dynamics. Ishibashi and Wald (IW) determined boundary conditions yielding well-posed dynamics with conserved positive energy for scalar, electromagnetic, and linearized gravitational fields, using nonlocal potentials and individual spherical harmonic modes. In this paper, we determine which IW conditions are local in the primary fields and which are AdS-invariant. In four spacetime dimensions, the standard AdS-invariant boundary conditions set the rescaled magnetic field to zero for electromagnetism and the rescaled magnetic Weyl tensor to zero for Einstein gravity on the conformal boundary. We generalize these standard boundary conditions by setting arbitrary linear combinations of the electric and magnetic fields, or the corresponding Weyl tensors, to zero, and we conjecture that these exhaust the local, AdS-invariant, conservative boundary conditions in AdS$_{1,3}$. Boundary conditions with non-AdS-invariance and in different spacetime dimensions are also studied. The AdS-invariant conditions in AdS$_{1,3}$ extend to Yang-Mills theory and nonlinear gravity in a general Fefferman-Graham setting. We construct phase spaces for these general boundary conditions. The covariant phase spaces for general conditions are naturally associated with Lagrangians containing Pontryagin terms and, in gravity, a Gauss-Bonnet term. In gravity, except for the standard boundary condition, no nontrivial asymptotic symmetries exist and all conserved charges such as ADM mass vanish identically, as in a closed universe. Spacetimes with Killing fields including AdS then exhibit linearization instability in the sense of Fischer and Marsden and Moncrief. For nonstandard boundary conditions, the modified symplectic structure yields new expressions for the entropy formula of black holes.

Bimetric theory is an extension of general relativity that perturbatively describes one massless and one massive graviton. It admits observationally viable cosmologies, passes local tests of gravity, and provides candidates for dynamical dark energy and spin-2 dark matter. Scattering amplitudes provide a complementary probe of its consistency, e.g. through analyticity, unitarity, and causality. While the tree-level $2\to2$ amplitudes of the closely related theory of massive gravity have previously been computed and analysed, the richer amplitude structure of bimetric theory has mostly been studied for selected processes and helicity sectors. We present the complete set of tree-level $2\to2$ scattering amplitudes of ghost-free bimetric theory around proportional Minkowski backgrounds. We expand the action through quartic order in the mass eigenstates and use a computer-algebra workflow to compute all of the $199$ symmetry-inequivalent helicity amplitudes. We find a clear hierarchy: amplitudes with a single massive external state vanish, those with exactly two are independent of the nonlinear bimetric parameters, and nonlinear ghost-free parameter dependence first appears with three massive external states. Taking the massive-gravity limit yields the complete set of tree-level $2\to2$ massive gravity amplitudes, which agree exactly with previous results. Finally, all amplitudes grow with energy at most as $E^6$, corresponding to the characteristic $\Lambda_3$ strong-coupling scale, and this maximal growth cannot be eliminated by any nontrivial choice of the theory parameters.

We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon, in stark contrast to what happens for massless fields. We also calculate the energy fluxes in Eddington-Finkelstein coordinates $\{u,v\}$. We show that these fluxes on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates $\{U,V\}$ the ingoing flux diverges like $V^{-2}$ on the Cauchy horizon (where $V=0$). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.

The Batalin-Vilkovisky (BV) framework is a powerful technique for quantizing a wide range of gauge systems. This formalism employs fields and antifields–introducing a symplectic structure through the antibracket–to implement BRST symmetry, which captures the essence of gauge invariance. Within this context, we study the symmetry structure of a pure Yang-Mills theory with universal extra dimensions. We construct a BRST-invariant extended action for the $(4+n)$-dimensional theory depending on fields and antifields, which constitutes a proper solution to the master equation. The higher-dimensional spacetime and gauge symmetries are then hidden within their four-dimensional counterparts via canonical transformations. Gauge invariances are fixed by combining gauge-fixing procedures for both the standard and Kaluza-Klein (KK) fields. This procedure is implemented covariantly in the adjoint representation of the gauge group. While the standard gauge fields are fixed using the Background Field Method (BFM), the KK gauge excitations are fixed covariantly, as they transform as matter fields. Finally, the manifest $SU(N)$ gauge symmetry of the quantized theory is emphasized.

We study the restricted fan cut inside the dual fundamental Weyl chamber by the weights of a $27$-dimensional minuscule representation of $E_6$; the two such representations are dual and give the same arrangement. Only $11$ of the $27$ weights have kernels meeting its interior, and we prove that they determine the entire fan. It has exactly $14$ chambers and $18$ extreme rays, every chamber is a six-dimensional simplicial cone, and we determine all facets, rays, and incidence relations. The chamber count was previously obtained by Diaconescu and Entin; the simplicial structure, extreme rays, and incidence data are new. The geometry of the $27$ lines on a cubic surface then explains and organizes the resulting chamber architecture. We also enumerate all faces, compute both characteristic polynomials—the arrangement is not supersolvable—together with lattice indices and projective chamber volumes, and describe the oriented matroid. Our main result is representation-theoretic. A distinguished $14$-element visible subposet of the minuscule $\mathbf{56}$ of $E_7$, defined entirely inside $E_7$, has Hasse diagram equal to the chamber adjacency graph of the $E_6$ arrangement. Three canonical $7+7$ splittings of it, of types $A_7$, $D_7$, and $E_7$, are the visible traces of Levi-center $\mathfrak{u}(1)$-charge decompositions of the $\mathbf{56}$ and reproduce the three level-$8$ decompositions on the $E_6$ side. More strongly, the simple-root labels on its covers, transported by minimal-length coset representatives, recover chamber by chamber all six facets and, globally, the $11$ active weight hyperplanes and the boundary walls of the dual Weyl chamber. Thus the $E_7$ shadow records not merely the chamber graph but, once matched with the independent $E_6$ classification, the full local wall architecture of $I(E_6,\mathbf{27})$.

We establish an obstruction to dimension-independent local color-kinematics duality for the one-loop six-gluon amplitude in pure Yang-Mills theory. The maximal and fivefold cuts admit a polynomial solution, but no allowed contact correction reproduces a required fourfold cut. We consider parity-even Lorentz-polynomial numerators, multilinear in arbitrary transverse external polarizations, with conventional quadratic propagators, global graph identities, and pointwise formal-color cut equality. No dimension-specific Gram identities are imposed. In the sector containing one polarization inner product, the higher cuts determine the complete remaining contact freedom. Every such correction obeys an exact coefficient relation that the required physical residual violates, independently of the chosen higher-cut solution. The violation is proportional to the transverse internal vector-state count and is nonzero at every nonzero value of its algebraic continuation. Momentum homogeneity extends the degree-six contradiction to all finite polynomial degrees. An all-multiplicity polynomial family retaining these representation conditions is therefore excluded.

We show that a formal deformation quantisation of degree-2 differential graded symplectic (QP) manifolds gives rise to the complete classical kinematics and dynamics of NS-NS supergravity, or, equivalently, its duality-covariant formulation as double field theory (DFT). Our construction extends the standard tensor hierarchy, encoding gauge parameters and their redundancies, to a complex encoding the physical fields, field strengths, and Bianchi identities. We present two realisations of such a complex: 1) a differential graded Lie algebra built from the algebra of functions on the QP-manifold; 2) a cochain complex that reproduces the tensor hierarchy representations conjectured in the literature and can be interpreted as a classical BV complex of the linearised theory. The deformation that gives rise to the dilaton comes from a normal-ordered graded Moyal–Weyl star product. This naturally extends the duality structure group from $\mathrm{O}(D,D)$ to $\mathrm{O}(D,D)\times\mathbb{R}^+$. Finally, our framework provides a direct route to constructing the DFT action via local double Lorentz invariance, and offers a transparent algebraic foundation for curvature tensors in generalised Cartan geometry.

The Sommerfeld enhancement (SE) from long-range interactions, and the related bound state formation rate, can be important non-perturbative inputs to dark matter (DM) annihilation signals. In the presence of singular interaction potentials, the conventional boundary conditions of the Schrödinger equation fail, obfuscating the computation of SE, its physical origin, and its relation to bound states in such potentials. In this work, we clarify the origin of SE in singular potentials in a two-fold manner: using the framework of velocity power counting in non-relativistic effective field theory (NREFT), and via position-space regularization of singular potentials at short distances to compute SE and bound states. We illustrate our findings through the case of pseudoscalar mediators interacting with massive Dirac DM. We find that when such a system arises from a UV-complete theory at weak coupling, no SE is generated. However, in the case of a derivatively coupled pseudoscalar, where the interaction is described by a higher-dimension operator in an effective theory, SE (and bound states) can occur for weak couplings if there is a large hierarchy between the cutoff scale of the effective theory and the dark matter mass. This SE is sensitive to the choice of the UV completion of the potential at short distances, but a non-negligible SE can persist even when the UV physics alone would not generate any SE; we elucidate the interplay of UV and IR physics in this case.

We study the representation theory of the vertex operator algebras (VOAs) associated with rank-one 4d $\mathcal{N} = 3$ superconformal field theories. For the $\mathbb{Z}_3$ S-fold theory, whose VOA $\mathcal{W}_{\mathbb{Z}_3}$ has central charge $c_{\mathrm{2d}} = -15$, we use the $\mathcal{N} = 1$ Lagrangian description to obtain the unflavored Schur index in terms of Dedekind eta functions, while Wilson-loop indices yield the unflavored non-vacuum characters. These characters all solve a modular linear differential equation (MLDE) whose solution space also contains a logarithmic character. Combining flavored MLDEs from null states with Zhu's associative algebra and a free-field realization, we study four highest-weight modules of $\mathcal{W}_{\mathbb{Z}_3}$ and their flavored characters in closed form. A parallel analysis applies to the $\mathcal{N} = 3$ theories obtained by gauging a discrete $\mathbb{Z}_n$ flavor subgroup of $\mathcal{N} = 4$ $U(1)$ and $SU(2)$ super-Yang–Mills, for which we also obtain closed-form Schur indices and a new free-field realization of the VOA of the $\mathbb{Z}_4$ quotient.

We associate a gravitational Hilbert space $\mathbf{H}_\sigma$ to any closed compact $(d-1)$-manifold $\sigma$ with real metric. A quantum state $\mathcal{J}(\sigma)$ is a $d$-manifold bounded by $\sigma$ and equipped with elliptic data. An inner product is defined by gluing states pairwise across $\sigma$ and evaluated by viewing the resulting closed $d$-manifold as a boundary condition on the gravitational path integral (GPI) over $(d+1)$-manifolds. If $\sigma$ is nonempty and the GPI is dominated by a single $(d+1)$-manifold $M$ in the $G_N\to 0$ limit, then $M$ contains a Lorentzian CRT fixed-point set, providing $\mathcal{J}(\sigma)$ with a classical spacetime interpretation. Conversely, given a finite Lorentzian domain with edge $\sigma$, a state $\mathcal{J}(\sigma)$ may be associated to it by deforming its initial data off the real Lorentzian section and retaining only elliptic data. This establishes a broad correspondence between non-asymptotic spacetime regions and quantum states. Assuming that $\mathbf{H}_\sigma$ factorizes over connected components of $\sigma$, our framework admits operators and partial traces. This allows us to explore the information-theoretic structure of the states we define. As an example, we construct a family of states by deforming partial Cauchy slices $\Sigma$ that straddle a two-sided black hole; $\sigma$ consists of two spheres. We construct the reduced state on one sphere and find that its Rényi entropies are positive, monotonic, and sensitive to all aspects of $\Sigma$ and its complex deformation. The von Neumann entropy, however, is controlled only by the maximin surface in the causal domain of $\Sigma$, independently of other parameters, so long as the complex deformation does not vanish. Our proposal may thus explain the efficacy of tensor network toy models of holography while transcending their limitations.

We construct and study lattice realizations of finite 2-group symmetries in ${2+1}$d quantum lattice systems with finite-dimensional tensor-product Hilbert spaces. We focus on two broad classes of 2-groups with 0-form symmetry group $G$ and 1-form symmetry group $A$: split 2-groups with trivial Postnikov class ${[\beta]\in\mathcal{H}^3(G,A)}$, and central 2-groups with trivial action ${\rho\colon G\to\text{Aut}(A)}$. In both cases, we construct symmetry operators on the full tensor-product Hilbert space that become 2-group symmetry operators when restricted to the topological subspace of the lattice $A$ 1-form symmetry. While the lattice split 2-group symmetry operators are onsite, the lattice central 2-group symmetry operators are not, and can only be made onsite after introducing ancillae. We extensively explore various manifestations of $\rho$ and $[\beta]$ for these lattice 2-group symmetry operators and demonstrate their agreement with expectations from quantum field theory. These manifestations arise in the transformation of operators carrying symmetry charge, the structure of lattice 2-group symmetry defects, and the dual fusion 2-category symmetries obtained by gauging the lattice 2-group symmetries. We further propose families of local symmetric Hamiltonians for both classes of lattice 2-group symmetries and identify exactly solvable limits lying in phases with spontaneous 2-group symmetry breaking and nontrivial symmetry-enriched topological order. In one such limit, the gauged Hamiltonians are exactly solvable lattice realizations of the corresponding 2-group gauge theories, whose ground-state degeneracies we calculate.

We study the phenomenology of the topological portal between QCD and pseudo-Nambu–Goldstone dark matter proposed in~\cite{Davighi:2024zip}. We construct a weakly coupled ultraviolet completion in which a vector mediator gauges a baryonic current of QCD for the light quark flavours, linking it to dark pions parametrizing the coset $SU(2)_D/U(1)_D$. As a concrete anomaly-free realisation, we gauge the leptophobic combination $B_1+B_2-2B_3$. This completion allows us to calculate thermal coannihilation beyond the regime of validity of the pion effective theory, including resonant mediator effects, and to test the resulting thermal target with boosted-dijet and monojet searches at the LHC, with LEP and bottomonium data, and with flavour observables. These collider signatures follow directly from the symmetry structure required by matching onto the topological portal. At low momentum transfer, the topological operator instead controls the decay of the heavier dark pion, which is long-lived. A future high-statistics $Z$ factory, such as FCC-ee, can probe the low-mass region where hadron-collider sensitivity deteriorates, providing complementary tests of the topological portal.

As parameters are varied, the set of saddle points contributing to a (path) integral may change discontinuously, leading to a corresponding change in the asymptotic expansion of the integral. This behavior is known as the Stokes phenomenon. We explore this phenomenon in the context of the analytic continuation problem relating the AdS/CFT and dS/CFT correspondences. In this paper, we study these correspondences for three-dimensional pure gravity and two-dimensional Liouville theory, using independent calculations in bulk minisuperspace and in the boundary Liouville zero-mode. In the bulk, the dS contour selects a single saddle and yields the tunneling wave function. Upon continuation to AdS, the contour instead selects an infinite family of saddles. The boundary calculation independently reproduces the same Stokes structure at leading semiclassical order, providing a nontrivial holographic consistency check. Our construction also offers a contour prescription for the conformal factor problem in Euclidean AdS$_3$ quantum gravity within minisuperspace.

In a broad class of inflationary models, the leading non-Gaussian bispectrum arises from one-loop rather than tree-level processes. However, realistic one-loop contributions remain largely unexplored for phenomenologically relevant masses beyond the simplest bubble diagrams. This is insufficient for observational purposes because, for generic masses and couplings, triangle contributions need not be suppressed relative to their bubble counterparts. We present a numerical method for evaluating scalar one-loop in-in diagrams contributing to the inflationary bispectrum at fully general external momenta and masses. First, the Witten-Feynman parameterization reduces de Sitter loop integrals to generalized Euler-Mellin integrals governed by Symanzik graph polynomials. Unfortunately, the exponents of the polynomials in the integrand become complex for sufficiently heavy masses, leading to sign problems when evaluating the integral using standard numerical techniques. To remedy this problem, we introduce the reduced Schwinger method, which evaluates a highly oscillatory subintegral analytically to obtain a Gauss hypergeometric kernel, leaving the remaining integrals to standard numerical quadrature. We validate the algorithm by reproducing known analytic results for the tree-level bispectrum in terms of ${}_3F_2$ functions, and then apply it to the one-loop bubble and triangle contributions at general kinematics. This yields the first direct numerical evaluation of the complete one-loop bispectrum, valid across the full kinematic range. Using these numerical results, we construct bispectrum templates and compare them with CMB data.