Papers

We study scale-separated AdS$_3$ models with full moduli stabilization in massive IIA supergravity on G2 orientifolds. In addition to constructing new examples, we investigate the properties of these models once the singularities of the G2 toroidal orbifold are resolved. The blow-up moduli are shown to be stabilized using fluxes in a parametric regime that preserves scale separation and control under the supergravity approximation. We further show that the apparent orientifold intersections in the singular orbifold description do not exist on such resolved spaces. Finally, we analyze the brane dual picture of such models using flux backtracking. We highlight several interesting features from such analysis such as a finite interval solution of the resulting flow equations in some of the models and the desirable low-energy decoupling of brane modes.

We present a new four-fermion model with a strongly non-polynomial coupling. To eliminate these non-polynomialities, we introduce two auxiliary vector fields and show that the dynamical Lorentz symmetry breaking is possible in our theory, as revealed by the effective potential generated for these vector fields. We explicitly calculate the low-energy effective action for these fields, which is given by the sum of three Maxwell terms (one for each field and a mixed one) plus a potential term displaying nontrivial minima.

The $SU(2)$ Skyrme model admits exact solutions when coupled to General Relativity in four spacetime dimensions. Here, we demonstrate that relevant gravitational configurations, such as black holes, wormholes, and cosmologies, are robust under the extension to $SU(N)$ with an arbitrary number of flavors. We show that key physical features, such as the thermodynamic properties, the baryon number of the configurations, and the geometry, are crucially determined by the number of flavors as well as the coupling constants of the theory. In particular: first, we prove that an increase in the matter content favors the local thermal stability of spherically symmetric black holes. Second, for cosmological solutions, we demonstrate analytically that as the hadronic matter content increases, the scale factor grows more slowly due to enhanced gravitational attraction, while the expansion rate (measured by the Hubble parameter) increases as a consequence of the higher energy density. Third, we find that the throat of traversable wormhole solutions can be enlarged by increasing the number of flavors, since the energy density required to keep the throat open does not grow indefinitely but rather saturates at a finite value.

We investigate holographic Krylov complexity in bottom-up holographic QCD models describing the confined phase, using the recently proposed correspondence between the growth rate of Krylov complexity and the proper radial momentum of probes, such as particles and strings, falling in the bulk spacetime. As representative confining backgrounds, we consider two horizonless geometries, namely the dilaton-deformed AdS-soliton and the deformed thermal-AdS spacetime, both arising as solutions of an Einstein-dilaton gravity system. We find that the Krylov complexity associated with a massive particle exhibits qualitatively distinct behavior in these two backgrounds when analyzed in the Einstein frame. In the deformed AdS-soliton geometry, the complexity undergoes periodic oscillations, with both the oscillation period and amplitude depending on the parameters of the model. In contrast, in the deformed thermal-AdS geometry, the complexity grows exponentially at late times and does not display oscillatory behavior. We then investigate string dynamics in the string frame and find that the Krylov complexity exhibits oscillatory behavior in both confining backgrounds. This behavior is traced to the emergence of an additional turning point in the deep infrared of the string-frame geometry. Motivated by this observation, we further analyze massive-particle dynamics in the string frame, where we find qualitatively similar behavior in the two confining backgrounds. Our results demonstrate that the Krylov complexity of confined holographic systems depends sensitively on the choice of probe and frame, while also revealing a closer correspondence between the two confining geometries in the string-frame description.

Understanding the gravitational interaction is one of the great scientific endeavors of the 21st century. The Nobel Prize-winning discovery of gravitational waves in 2015, and subsequent detections by the LIGO-Virgo-KAGRA Collaboration, have marked a revolutionary step forward in physics and astrophysics by opening an entirely new window for exploring the Universe. Future upgrades to these detectors, along with upcoming facilities such as LISA, the Einstein Telescope, and radio and optical instruments, promise other breakthrough discoveries that the next generation of scientists will need to interpret. The School on Gravity (22–26 June 2026, Copenhagen) aimed to introduce junior scientists–graduate students and advanced undergraduates with a background in general relativity–to a wide range of foundational topics in the exciting new field of gravitational-wave physics. Topics spanned from the theory of motion, to new challenges introduced by quantum physics, to the astrophysics of black holes and source modeling for gravitational-wave detectors. The School on Gravity took place at the legendary Auditorium A of the Niels Bohr Institute, inviting students and lecturers to challenge current paradigms in gravitational physics in the spirit of the quantum revolution that unfolded in this very room. These lecture notes aim at opening up those new ideas presented in Auditorium A to the rest of the scientific community.

We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called $\nu$-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to $T\bar{T}$-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify $T\bar{T}$ as the only deformation that can be interpreted as a field-dependent coordinate transformation.

While naively simpler than its higher dimensional cousins, 2d physics still has its own share of puzzles. An example of this is instances of dualities of $(0,2)$ theories, passing all consistency checks save for a mismatch in global symmetry. This is common when said duality can be motivated by dimensional reduction of a duality of 4d $\mathcal{N}=1$ theories where said symmetry emerges in 2d, often from an anomalous 4d symmetry. It is commonly believed that these symmetries are broken in the 2d theory, though often the mechanism for such breaking is not understood. We examine various appearances of this phenomenon and show that in these cases the elliptic genus shows signs of the presence of marginal operators that can break these symmetries. Interestingly, these operators do not appear perturbatively but emerge from the calculation, raising the question of what operators the $(0,2)$ elliptic genus actually counts. This provides a potential mechanism to overcome the discrepancy in symmetry, though we point out some potential subtleties.

We show how the covariant phase space Hamiltonian can be constructed in theories in which some of the fields have gauge freedoms. The addition to the action of boundary terms that guarantee the well-posedness of a variational principle and its exact gauge invariance for the prescribed boundary conditions turn out to be essential in this construction. The same ingredients are essential in the use of the action in the framework of Gibbons and Hawking's Euclidean approach to Quantum Gravity and we show how the on-shell action constructed with a Lagrangian with those properties can be expressed in terms of the covariant phase space Hamiltonian. We compute the Hamiltonian of several theories, one of which has Chern–Simons terms, using our prescription and show that, in black-hole backgrounds, the Hamiltonian gives directly the quantum statistical relation including terms related to non-gravitational charges and chemical potentials, as expected.

Chiral gauge theories are a central focus of research in theoretical particle physics due to the parity symmetry breaking observed in the Standard Model. Left-Right Symmetric Models (LRM) explain the breaking of parity through a Spontaneous Symmetry Breaking Mechanism, predicting new $W_R$ and $Z_R$ gauge bosons. The absence of direct BSM physics detection at the LHC has driven research towards precision observables and Effective Field Theories (EFTs), particularly the SMEFT framework. Precision radiative calculations in chiral theories using dimensional regularization require a $D$-dimensional $\gamma_5$ prescription, such as the mathematically consistent Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme. However, this scheme introduces gauge symmetry-breaking terms that obstruct Slavnov-Taylor identities. A primary objective of this thesis is to provide a pedagogical introduction to cancelling these spurious anomalies via algebraic renormalization, and to derive the one-loop symmetry-restoring finite counterterms required to renormalize the four-fermion operators of the $\nu$SMEFT. Furthermore, the thesis explores UV completions like LRMs embedded in other BSM theories like the Grand Unified Theories. This embedding implies that no discrete symmetries remain at the TeV scale and allows LRMs to be treated as EFTs with the minimal scalar content needed to perform the Spontaneous Symmetry Breaking Mechanism. The second main objective is to derive robust lower bounds on the masses of the new gauge bosons and the LR scale using collider observables. This analysis is performed for both the effective and traditional LRMs, ensuring that the results are independent of other parameters of the theory.

We discuss General Relativity and some of its modifications as effective field theories of the breaking of the affine general linear group using the coset approach and the Maurer-Cartan form. While the ultimate goal is to break the symmetry down to the Lorentz subgroup, we argue that there are three interesting breaking cascades in which the affine general linear group is first broken to a larger subgroup that contains the Lorentz group. In all cases, the breaking of translations always generates Goldstone modes that can be interpreted as metric degrees of freedom. We argue that the effective field theories that emerge as a result of the different breaking patterns are all dynamically equivalent at the lowest order of the derivative expansion, e.g., using Einstein-Hilbert-like actions, but can differ beyond the leading order.

Holographic complexity is expected to capture the linear growth of black hole interiors, with quantum corrections ultimately leading to a late-time saturation. We develop a spectral formulation of holographic complexity measures associated with codimension-zero bulk regions in the framework of the complexity=anything proposal. The corresponding generating function of complexity is governed by three-point correlation functions of the density of states, establishing a direct connection between bulk geometric observables and nonperturbative Euclidean spacetime wormholes. We find that the codimension-zero holographic complexity reduces to the sum of two codimension-one contributions and exhibits a universal time evolution, characterized by an exponentially long regime of linear growth followed by saturation at the Heisenberg time. The late-time plateau is a direct result of the spectral level repulsion, a generic feature of quantum chaotic systems, thereby providing a universal mechanism for the saturation of holographic complexity. We also develop a complementary operator interpretation, in which Euclidean wormhole corrections render the semiclassical basis of fixed-complexity states overcomplete. Constructing a complete orthonormal basis then yields well-defined holographic complexity operators that reproduce the same universal time evolution. Our results establish a unified connection among black hole interiors, chaotic spectral statistics, and Euclidean wormholes in quantum gravity.

Recent numerical simulations have shown that black-hole magnetospheres evolve rapidly toward alignment between the magnetic axis and spin axis but the physical origin of this process has remained unclear. We develop an analytic theory of this alignment within resistive relativistic magnetohydrodynamics. Taking the slow-spin Blandford-Znajek monopole solution as the exterior magnetic field, we reduce the induction equation to a relaxation equation for the current-sheet inclination angle. Our analysis shows that alignment results from second-order spin effects in the Blandford-Znajek solution combined with explicit resistive dissipation. We test this prediction using resistive-GRMHD simulations at several spins and resistivities and find a regime in which the measured late-time secular decay agrees quantitatively with the analytic prediction.

We formulate perturbative Jackiw-Teitelboim gravity as an ensemble of ordinary one-dimensional Hamiltonians with a confining random potential. The leading profile reproduces the disk density of states, while connected cumulants of a single master field encode the topological expansion. After formulating the cumulant power counting required by the topological expansion, we show that the cumulants reproduce all genus-zero multi-boundary amplitudes $\mathcal Z_{0,n}$. At higher genus, we show that a renormalization scheme can be chosen consistently order by order so that imposing one-boundary polynomiality recursively reproduces the perturbative JT string equation and yields the standard JT one-boundary amplitudes $\mathcal Z_{g,1}$. The framework provides a self-contained finite-$S_0$ quantum dynamics with a discrete spectrum and unitary real time evolution, beyond a mere rewriting of the matrix integral. The same confining dynamics also underlies late-time saturation and the dynamical avoidance of the would-be black hole singularity, as shown in our earlier work.

We investigate the Casimir effect between two parallel wires in $(2+1)D$ Maxwell-Chern-Simons (MCS) electrodynamics under different boundary conditions and separated by a distance $L$. Using a functional approach in which the boundary constraints are implemented by auxiliary fields localized on the wires, we integrate out the gauge field and derive an effective boundary theory whose functional determinant allows us to compute the Casimir energy. We consider perfect electric conductor (PEC), perfect magnetic conductor (PMC), and infinitely permeable (PMC2) boundary conditions. For two PEC wires, we recover the known MCS result and show that it coincides with the result obtained in the Abelian limit of the Curci-Ferrari (CF) model, implying that the Casimir effect in this case probes the photon mass $\mu$ but not its origin. The same energy is obtained for two PMC2 wires. In sharp contrast, the Casimir energy vanishes identically for the covariant PMC condition in MCS theory, both for PMC-PMC and PEC-PMC. Since this cancellation does not occur in the CF model, it could provide a signature of the topological origin of the photon mass in $(2+1)D$. Finally, the PEC-PMC2 case yields a non-vanishing Casimir force and reproduces the known result for a perfectly conducting wire facing an infinitely permeable one. Interestingly enough, we show that for PEC-PMC2, the Casimir force in the MCS theory is smaller than the one of the CF model for any $L,\mu >0$. Our results thus show that, depending on the boundary conditions, the Casimir effect could probe not only the photon mass but also reveal signatures of its origin.

We analytically study the peak statistics of an amplitude ensemble to identify the local mechanism responsible for peak repulsion. Our analytical approaches show that a smooth, nondegenerate ensemble of sufficiently differentiable amplitudes exhibits quartic nearest-neighbor repulsion, $p_{\rm nn}(S)\sim S^4$, where $S$ is the spacing between adjacent peaks. We verify this prediction numerically for the tree-level highly excited string scattering amplitudes. Interestingly, we find the quartic repulsion to be robust by varying both the underlying ensemble and the amplitude functions, whereas a tunable cusp model shows that weakening differentiability changes the strength of the repulsion. Peak repulsion therefore defines a local universality class that is not unique to string theory and may occur in amplitude ensembles in other theories.

We study open strings in a constant magnetic field from the viewpoint of universal canonical variables. Using a conserved Klein-Gordon-type pairing, we show that the canonical commutation relations remain background independent in the distributional sense, while the background dependence is encoded in the mode representation. The Bogoliubov transformation between different magnetic backgrounds is not unitarily implementable, so that the corresponding Fock representations are inequivalent. Nevertheless, the transformation determines the relative normalization of the vacua. We show that the resulting relative vacuum normalization precisely reproduces the relative boundary $g$-function, or equivalently the magnetic-field-dependent part of the disk amplitude, and yields the Dirac-Born-Infeld factor. Thus the disk normalization is encoded directly in the transformation between inequivalent representations of universal open-string variables.

Three-dimensional Einstein gravity has no local degrees of freedom, yet retains rich global and black-hole physics. Adding a scalar normally spoils this. We show that closure of three-dimensional Horndeski gravity under disformal field redefinitions selects a square-root curvature interaction. A nonlinear analysis finds no local bulk modes on regular branches, while an independent Hamiltonian analysis confirms the result on the timelike-gradient branch. This extends the no-local-bulk-dynamics paradigm beyond pure Einstein gravity and motivates studying its boundary and global sectors.

Geometric Inflation adds an infinite tower of curvature invariants to the Einstein-Hilbert action while preserving certain key features such as leading to second order modified Friedmann equations for FRW backgrounds. Sourcing them with a perfect barotropic fluid can easily produce a slow-roll inflationary regime, no inflaton field is required. In this work, we perform the Wheeler-DeWitt quantization of minisuperspace Geometric Inflation models. First, we construct an effective 1D FRW action and perform the Hamiltonian formulation using both Ostrogradsky's approach and Dirac's algorithm for constrained systems. The Lagrangian and Hamiltonian treatment of the perfect fluid is based on Schutz's formalism. Second, we postulate the Wheeler-DeWitt equation and investigate its solutions both analytically and numerically. For radiation we are led to a system of fractional differential equations for which we use Caputo fractional derivative operator. We construct wave packets in momentum space, with the fluid's variable acting as external time parameter.

We examine the response of a two level Unruh-DeWitt (UD) detector interacting with the Kaluza-Klein (KK) mass modes of a bulk scalar field in extra dimensional models. Considering two of the promising extra dimensional models with distinct compactifications, such as large, flat extra dimensions in the Arkani Hamed, Dimopoulos & Dvali (ADD) framework and warped extra dimensions in the Randall-Sundrum (RS) scenario, we compute the profile function of the detector. We extend this computation to the 6 dimensional doubly compactified spacetime geometry. The profile function of the detector has been examined as a function of the energy gap of the detector, the compactification radius of the extra dimension, and the dimensionality of spacetime, requiring the chosen parameter space appropriately such that the gauge hierarchy problem is duly addressed. We find that the pattern of the profile function is dictated by the spacing of the KK mass spectrum and the resolution of the detector. For ADD model, the spacing between successive KK modes decreases with the increasing compactification radius, yielding a smoothly increasing continuum pattern in the profile function. Whereas for the RS warped geometry model, a tiny deviation in the radius of the extra dimension produces a large change in the same, resulting a sharp increment. The resolvability of the KK mode structure is sensitive to the underlying geometry of the spacetime, providing a qualitative distinction between flat and warped extra dimensional scenarios within the UD detector framework.

We construct a geometric theory on the brane space $S^2M=C^\infty(S^2,M)$ associated to a gerbe with connection on $M$. Normalized logarithmic holonomy around the latitude circles defines an average holonomy line bundle on the brane space, whose connection and averaged flux give an equivariantly flat superconnection. We prove that the completed periodic exotic twisted cohomology defined by this superconnection localizes to the twisted cohomology of $M$. This brane space localization happens in two stages: circle localization lands on the free path space of $M$, and contracting the paths, after a correction of the twisting form, brings us back to $M$. Parallel transport along the meridians lets us average gerbe module connections, after which the circular iterated-integral construction applies. The resulting twisted brane Bismut-Chern forms restrict to the twisted Chern forms on $M$; their variation is described by twisted brane Bismut-Chern-Simons forms. For a T-dual pair, transporting the classical Hori morphisms through localization yields graded genus-0 T-duality on brane cohomology. The composite of each morphism with its dual is minus the Euler operator in the level variable, so these morphisms are isomorphisms at every nonzero level. At level one these morphisms are compatible with the brane character and twisted $K$-theory T-duality.

We calculate the spectrum of gravitational waves generated by a cosmological magnetic field with a narrow-band power spectrum. For a spectrum narrowly peaked at a comoving wavenumber $k_c$, we find that the gravitational wave signal peaks at $2k_c$ and has a sharp cutoff at this scale. We apply this result to an ultralight dark matter model of magnetogenesis operating around recombination, in which an axion-photon coupling generates a helical magnetic field by parametric resonance. We determine the conditions for the resulting gravitational waves to enter the frequency range of pulsar timing experiments. Although the required frequency can be reached for sufficiently large coupling, the corresponding amplitude is below the experimental sensitivity for physically allowed energy densities of the magnetic field. We generalize this conclusion to models of magnetogenesis operating at other epochs, estimating as $T \simeq 160 \mathrm{MeV}$ the temperature of a magnetogenesis process assumed to be the source of the stochastic gravitational wave background suggested by pulsar timing arrays. We place the lower bound $T \gtrsim 1$-$10 \mathrm{MeV}$ on such viable models.

Do lattice triviality, suspected Borel non-summability and the perturbative Landau pole exclude an interacting four-dimensional theory satisfying the Osterwalder–Schrader axioms and reproducing every renormalized coefficient of positive-coupling $O(N)$ $\phi^4$ theory? An example involving one real function separates vanishing cutoff limits along its allowed bare trajectories from a nonzero result obtained by renormalizing the coefficients first; an exponentially small correction preserves its expansion and removes the pole in its running coupling. For the massless two-point expansion of the singlet composite $\Phi_a\Phi_a$ at leading order in $1/N$, ordinary Borel summation fails even for Gaussian smearing. The arithmetic mean of two Borel integrals along opposite imaginary rays defines a real distribution on every four-dimensional Schwartz momentum or position test, with finite-order remainder bounds uniform on bounded test sets. Two alternative covariances with nonnegative mass spectral weights remove the Euclidean pole and construct generalized free fields. After a fixed contact subtraction, their Euclidean extensions preserve every coefficient of the collective correlations obtained by Wick pairing. The interacting finite-$N$ family remains open. We also state a conditional interacting route through the physical scalar correlations of a larger theory (the parent) with heavy particles. A concrete $N=1$ gauge–Higgs–fermion candidate has a tuned one-loop trajectory on which all interaction couplings tend to zero in the ultraviolet, and a stable tree vacuum with additional masses comparable to the heavy scale. Constructing the parent and its corrected ultraviolet trajectory, and proving coefficient decoupling and the exact remainder bounds as the quartic coupling tends to zero and the family's heavy masses grow, remain open.

A tropical quantum field theory is an exactly solvable deformation limit of an ordinary QFT, governed by a non-linear partial differential equation. We use the integrable two-dimensional sine-Gordon theory as a testbench to compare the exact features of an undeformed model with its tropical counterpart. We classify scale-invariant tropical QFTs in $D=2$ and leverage functional renormalization group methods to demonstrate that all scale-invariant theories with periodic effective actions are infrared fixed points of flows originating from sine-Gordon Lagrangians. For the tropical sine-Gordon model, we compute the $\beta$-functions exactly, solve the renormalized theory both via a convergent expansion and numerically for all admissible couplings, and illustrate the complete renormalization group flow from the Gaussian to the IR fixed point. Finally, we study the large-order behaviour of the loop expansion and relate it to the Hamilton-Jacobi equation, whose solutions we interpret as tropical instantons.

The S-matrix bootstrap restricts low-energy interactions through unitarity, analyticity and crossing symmetry. For effective field theory couplings, positivity bounds have a natural geometric formulation, the EFThedron, in which the allowed couplings form the classical positive moment problem. We show that this geometry extends to full nonlinear unitarity. Multiplying the amplitude by fractional powers of the energy turns its real part into a moment as well, so that unitarity becomes a bounded complex moment problem. Analyticity becomes a set of linear constraints requiring different kernels to reconstruct the same couplings, analogous to the null constraints imposed by crossing symmetry. In two dimensions the problem can be solved exactly, leading to Castillejo–Dalitz–Dyson amplitudes as extremal measures of the moment problem. In four dimensions we obtain closed-form and semi-analytic bounds for the massless EFThedron model and for massive scalar scattering. For massive scalars, the analyticity constraints improve on published dual bounds, reducing the gap to the primal region. By placing the real and imaginary parts of amplitudes on an equal footing, the Real EFThedron provides a powerful framework combining unitarity, analyticity and crossing, opening a new route to mapping the space of consistent quantum field theories.

We study symmetries and anomalies of dissipative Majorana chains described by Lindblad dynamics. Using the operator-state mapping, we represent the Lindbladian as a non-Hermitian operator on a doubled Hilbert space. In this formulation, the ket and bra contours admit strong fermion parities and strong translations, while their diagonal combinations define weak symmetries. For even and odd chain lengths, we diagnose anomalies by comparing symmetry algebras with and without weak fermion-parity defects. These algebras retain the lattice precursor of the modulo-$8$ anomaly of the closed Majorana chain and exhibit projective relations between strong fermion parity and weak translation, as well as between weak fermion parity and strong translation, which are intrinsic to open quantum systems. We establish the IR correspondence between the lattice symmetry algebras and those of the doubled Majorana CFT in four spin sectors, identifying chiral fermion parities emanated from the lattice translations. Finally, we develop the lattice bosonization of the dissipative chain. For even length with collective energy dephasing, combining the defect and no-defect sectors and imposing GSO projections gives rise to an Ising Lindbladian with non-invertible Kramers–Wannier symmetries descending from the anomalous strong translation and fermion parity of the Majorana chain. For odd length, constructing mutually commuting ket- and bra-sector spin operators instead yields an Ising Lindbladian with a Kramers–Wannier duality defect. Our results provide a controlled framework for extending lattice anomalies and non-invertible symmetries to open quantum systems.

We argue that no material can be made completely transparent to light as long as it has a nontrivial index of refraction. The quantum decay of photons into phonons is an ineliminable source of attenuation. This survives even once all other excitations have been gapped away, impurities have been removed, and the temperature has been set to zero. Restricting for simplicity to the case of a superfluid, we determine via effective field theory methods the corresponding low-frequency contribution to the imaginary part of the index of refraction. This scales as $\omega^4$ and induces a nonanalyticity of the real part for $\omega \rightarrow 0$. We also extend our result to large coherent electromagnetic fields, such as those of a laser, showing that the effect can receive strong nonlinear enhancements. Our result is a genuine quantum lower bound to the transparency of a medium.

Universal horizons trap even arbitrarily fast signals, providing a test of black-hole thermodynamics in theories with a preferred time direction. In Einstein–aether theory, this direction is defined by a dynamical field, the aether, that can remain non-aligned relative to stationary time at infinity. In particular, for asymptotically anti-de Sitter black holes, it was so far impossible to recover a first law of black-hole mechanics when such asymptotic tilt of the aether is present. Here, we resolve this issue for an exact family of static, spherically symmetric solutions. Using the covariant phase-space formalism, we identify the asymptotic tilt and the decaying part of the aether field as a boundary source and its conjugate response. Allowing both to vary independently obstructs the definition of an energy that generates time translations. Fixing either quantity, or imposing a relation between them, restores such an energy, while externally varying the boundary data introduces work into the first law. The energies obtained by fixing the source or its response are related by a Legendre transformation. At the universal horizon, heat includes both the metric area contribution and an irreducible aether energy flux. The resulting balance separates work at infinity from horizon heat and explains why the physical temperature cannot generally be inferred from the coefficient of an area variation in the black-hole mass.

Gauged Linear Sigma Models (GLSMs) have long been a key tool in understanding Calabi-Yau compactifications of string theory. While descriptions of complete intersections of polynomial defining equations have long been understood in this context, a full treatment of non-polynomial complex structure deformations has been absent from the literature. Likewise, the somewhat more exotic generalized complete intersection Calabi-Yau construction has resisted a GLSM description. In this paper we resolve both of these omissions using completely standard GLSMs with polynomial superpotentials. The non-polynomial structure seen in the geometric constructions only arises in the associated GLSM upon restriction to the vacuum space of the theory. This feature enables the construction to avoid singularities in field space that could have arisen if non-polynomial structure were incorporated directly into the GLSM superpotential.

The OSV conjecture relates the helicity supertrace of black holes in $4d$ $\mathcal{N}=2$ supergravity obtained through a Calabi–Yau compactification of Type IIA string theory to the modulus squared of the topological string partition function evaluated at the attractor point in moduli space for a given set of magnetic black hole charges and electric chemical potentials. We find Euclidean black hole saddles that compute this index to all orders in the 4d supergravity derivative expansion and calculate their action using equivariant localization. The gravitational on-shell action localizes entirely to the north and south poles of each black hole, with the two contributions determined by the holomorphic and anti-holomorphic topological string free energies, respectively, evaluated at the attractor values of the moduli. For single-center black hole saddles, this provides a proof of the OSV conjecture to all orders in the topological string coupling. The same localization formula also applies to all saddles that contribute to the helicity supertrace, such as multi-center black holes, which leads to a non-perturbative refinement of the conjecture.

We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, $S^4$. Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless $\lambda\phi^4$ theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of $\lambda$. At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.