Papers

We prove existence, uniqueness and structure results for complete noncompact 7-dimensional G2-holonomy metrics with ALC (asymptotically locally conical) asymptotics. We regard such spaces as G2-analogues of ALF gravitational instantons in 4-dimensional hyperkähler geometry. Our main results include the existence of a G2-analogue of the Atiyah-Hitchin metric in 4-dimensional hyperkähler geometry, the existence of a good moduli theory for ALC G2-holonomy metrics and rigidity results for ALC G2-metrics in terms of the symmetries of their asymptotic model. The analytic toolkit needed to prove all these results is a robust Fredholm theory for the natural geometric linear elliptic operators on ALC spaces. We provide a self-contained derivation of this Fredholm theory for arbitrary Riemannian manifolds with ALC asymptotics. Since our ALC Fredholm theory does not rely on imposing any holonomy reduction or curvature conditions it may also be of utility beyond the setting of ALC special holonomy metrics. As one such application of our general Fredholm theory we prove some Hodge-theoretic results on general ALC spaces.

We investigate an analytical framework for reconstructing bulk geometries from pole-skipping data. Previously, this method enabled the recursive recovery of near-horizon metric derivatives in static, planar-symmetric black holes. Building on this framework, we systematically extend it to more intricate geometries, specifically static topological black holes and rotating black holes. For three-dimensional rotating black holes, we demonstrate that the metric can be fully reconstructed from boundary pole-skipping data. For four-dimensional rotating spacetimes admitting a separable coordinate system (such as the Kerr family), standard near-horizon pole-skipping successfully reconstructs the purely radial metric functions. To recover the remaining angular metric functions, we introduce a mathematical counterpart termed "angular pole-skipping," defined via a near-axis analysis. Although its precise holographic dictionary remains an open question, this bulk-side formalism completes the geometric reconstruction algorithm. Furthermore, we demonstrate that the vacuum Einstein equations can be recast as a set of algebraic equations governing the pole-skipping data and that the null energy condition imposes algebraic inequalities on this boundary data. Finally, we establish general polynomial constraints dictated by the overdetermined nature of the metric reconstruction, highlighting the highly redundant encoding of bulk geometry in boundary data.

We propose an effective Hamiltonian formulation of quantum field theories using a Daubechies wavelet basis in position space. Combined with flow-equation methods of the similarity renormalization group (SRG), this approach provides an efficient framework for analyzing quantum field theories by reducing the dimensionality of the Hamiltonian and systematically decoupling degrees of freedom across scales. As an application, the free scalar field theory has been reformulated within this framework to calculate the low-lying energy spectrum of the theory. These basis elements are known to transform the free scalar field theory into a theory of coupled localized oscillators, each of which is labeled by a location and a resolution index. In this representation, the Hamiltonian is naturally organized into fixed-resolution blocks, alongside blocks associated with the interactions between different resolutions. To decouple the different resolution modes and obtain a block diagonalized Hamiltonian with each block associated with a fixed resolution, the flow equation approach of SRG is applied. Finally, we demonstrate that with increasing resolution, the low-energy spectrum can be extracted from the effective lowest-resolution block of the Hamiltonian, leading to a significant reduction in computational cost.

We develop integration-by-parts (IBP) reduction and differential equations for massive loop integrals of cosmological correlators in de Sitter (dS) spacetime, demonstrating the feasibility of this approach. We identify a structural property of the dS IBP system: for an $n$-propagator family, it splits into $2^n$ closed subsystems classified by the parity of the propagator indices. We further formulate a Baikov representation for loop integrals in dS space and derive the corresponding dimensional recurrence relations. In flat spacetime, intersection theory shows that $\mathrm{d}\log$-form master integrands lead to $\mathrm{d}\log$-form differential equations. Motivated by fibration intersection theory, we conjecture that this construction extends to dS integrands involving Hankel functions. We verify this conjecture in the one-loop bubble family and determine the associated alphabet.

We derive the density of states and $2$- and $4$-point functions of embedded ensembles for both fermions and bosons in the double-scaled limit. It is shown the models are equivalent to the double-scaled Sachdev-Ye-Kitaev model, expanding the double-scaled universality class to include both fermionic and bosonic systems. The models can be solved by introducing the Wick product of non-commuting Gaussian random variables. We show that deriving the Wick product is sufficient for computing the density of states, and properties of the Wick product can be used to compute $n$-point functions directly in the energy basis. In this context, the Wick product is equivalent to normal ordering of $q$-oscillators, which leads to the duality between moments of double-scaled models and expectation values in the chord Hilbert space. By considering operator probes as a second set of oscillators, we extend the duality to compute $n$-point functions. Embedded ensembles are equivalent to complex SYK at fixed charge, and we show working directly with embedded ensembles streamlines the derivations.

In low-energy supergravity treatment of type IIB superstring on general D-instanton wormhole profiles in the bulk, we obtain non-vanishing scalar two-point functions in addition to the vanishing $\langle \tau^* \tau^* \rangle$ that corresponds to the BPS amplitude detected by two D-instantons at their respective boundaries. This is exploited to show that the modes of broken local supersymmetry in the bulk deliver the fermionic (diagonal) modes on the boundaries through the deformation by the form of current-current two point functions propagating on the tree level cylinder geometry. Our treatment is generalizable to multi D-instanton cases and general Euclidean branes.

We revisit the proposal to cure the negative density of states in the three-dimensional gravitational path integral by adding spinning states whose spin scales with the central charge. We show that sub-extremal and extremal spinning states below the black hole threshold, together with certain overspinning states above it, can cancel the known negativities in the spectrum. We interpret the states below threshold as bulk spinning defects. The overspinning states were previously interpreted as classical spinning strings; here we instead study their realization as maximal, fixed-point-free BTZ quotients. All of these spinning geometries exhibit causal pathologies in their Lorentzian continuations. The overspinning geometries arise from mixed elliptic–hyperbolic identifications and possess one formally real chiral temperature. We derive the extremal scalar correlator and propose a quotient-motivated image expression for the overspinning background.

There has been considerable interest in constructing modified gravity theories that propagate only two degrees of freedom (DOFs), corresponding to the tensorial gravitational waves of general relativity. Within the framework of spatially covariant gravity (SCG), the conditions for obtaining 2-DOF theories can be derived from Hamiltonian constraint analysis, but it is generally difficult to translate those conditions into explicit SCG Lagrangians, especially when the Lagrangian depends nonlinearly on the extrinsic curvature. In this work, we adopt an alternative perturbative approach. We consider polynomial-type SCG Lagrangians up to $d=3$, where $d$ denotes the total number of derivatives in each monomial, and expand them around a cosmological background. By requiring the scalar mode to be eliminated up to cubic order in perturbations, we derive the corresponding conditions on the coefficient functions in the Lagrangian. We find five explicit Lagrangians that propagate only 2 DOFs up to cubic order in perturbations around a cosmological background. These theories therefore provide concrete candidate 2-DOF SCG models, at least at the perturbative level up to cubic order.

Many body gravity (MBG) is a novel modified theory of gravity formulated in a 5-D space-time-temperature framework, in which the variation in temperature is recast as a variation in the 5-D metric. Previous work on MBG has shown that it can reproduce galaxy rotation curves, radial acceleration relation and the weak gravitational lensing of the bullet cluster, without the inclusion of dark matter. In this work we show that MBG can reproduce cosmic inflation, and in the process, analyze fundamental relations between interaction, time and gravity. To analyze cosmic inflation using interacting massless scalar fields, we first analyze theoretically a hypothetical universe with a single massive particle, or a collection of non-interacting massive particles. A quantitative relation between time and interaction is developed using Quantum Field Theory (QFT), which suggests that the notion of time becomes ill-defined for such a universe. The mass terms in MBG and General Relativity cause a discrepancy with the QFT results. An interacting massless scalar field then becomes a necessity to resolve the issue at the onset of inflation. However, the entropic terms in the MBG field equations are seen to be consistent with the QFT results and further accelerate inflation. The slow-roll condition is shown to be a natural consequence of the Euler-Lagrange equations of motion governing the massless scalar field in 5-D space-time-temperature, during the early phase of inflation. Finally, the MBG field equations are solved in the context of a Friedmann metric, leading to inflation. The matter era is also investigated.

The Unruh effect establishes that the Minkowski vacuum, when restricted to a Rindler wedge and described in terms of boost eigenmodes, satisfies the Kubo-Martin-Schwinger (KMS) condition and is therefore perceived as a thermal state by uniformly accelerated observers. This result is robust and remains valid for both massless and massive fields. In this work, we investigate a distinct geometric setup involving two null-shifted, nested Rindler wedges $R_2 \subset R_1$, where the standard assumptions underlying the Unruh effect are not directly applicable. We analyse how the Rindler vacuum defined with respect to $R_1$ is represented in terms of mode functions adapted to $R_2$ by computing overlap coefficients defined through projection of field modes along null directions. Owing to the absence of a common global Cauchy surface for the nested wedge pair, these coefficients are defined in a formal sense and do not correspond to a unitary Bogoliubov transformation between complete Fock spaces. Our results show that the projected mode content exhibits nontrivial mixing, but this does not constitute a violation of the KMS condition nor a modification of the standard Unruh effect. Instead, it reflects the limitations of defining particle content through partial, null-based projections in a restricted geometric setting. The analysis is carried out for both scalar and Dirac fields, with particular attention to the role of mode structure, inner products, and consistency conditions.

We develop a rigid $\mathscr{N} =(1,1)$ superspace framework for spatially inhomogeneous impurity deformations in $D=1+1$ dimensions by embedding the impurity profile into a real background superfield (spurion). This spurionic completion provides a manifestly supersymmetric description at the level of the action and offers a systematic route to identify which inhomogeneous backgrounds preserve a nontrivial subset of supercharges. Focusing on static interface-type configurations, we determine the half-BPS condition on the spurion background and the corresponding supersymmetry projector. In the resulting half-BPS sector we derive the associated first-order BPS equation for static bosonic matter configurations and establish an exact Bogomol'nyi completion of the static energy, yielding a sharp bound saturated by BPS solutions. We further comment on how explicit coordinate dependence and derivative-dependent impurity couplings can obstruct the Bogomol'nyi structure, thereby motivating spurionic extensions that retain supersymmetric control over inhomogeneous deformations.

While conventional oscillation experiments measure neutrino mixing parameters with high precision, these measurements are strictly confined to sub-TeV scales. At higher energies, renormalization-group effects can cause these parameters to evolve with the transferred momentum, $Q$. High-energy and ultra-high-energy astrophysical neutrinos, spanning TeV to EeV energies, probe high values of $Q$ unreachable by conventional experiments, offering an unprecedented test of high-energy mixing. We use the flavor composition of these neutrinos – the relative proportions of $\nu_e$, $\nu_\mu$, and $\nu_\tau$ – to constrain this evolution, both phenomenologically and within dimension-6 Standard Model Effective Field Theory. We account for astrophysical uncertainties – an unavoidable requirement to obtain realistic results, even though this weakens the bounds. Although present IceCube measurements lack the sensitivity to detect this running, we forecast that upcoming multi-detector combinations will place unprecedented bounds on the high-energy evolution of neutrino mixing.

Recent work has emphasized a subtlety of large- $N$ limits in AdS/CFT: a sequence of pure states in the microscopic theory need not remain pure with respect to the emergent algebra of observables. We study this phenomenon for Kourkoulou-Maldacena (KM) states in the double-scaling limit of the SYK model, and show that their ensemble-averaged algebraic description depends crucially on which observables survive the limit. For fermionic operators of size $N^{1/2}$, generic operators converge to the usual chord operators of double-scaled SYK. The resulting von Neumann algebra is the standard Type II$_1$ factor, and the KM pure states at infinite temperature converge to the tracial state, so generic probes lose access to microscopic purity. We then identify a class of operators adapted to the KM state that also survives the double-scaling limit. Since the KM state may be viewed as a projection inside the tracial state, these become dressed chord creation and annihilation operators. Once included, the limiting algebra becomes Type I$_\infty$ and the limiting state becomes pure. This gives a concrete example in which adding a sufficiently state-adapted operator to the emergent algebra restores access to the purity of the underlying state. We further show that correlators of the dressed operators admit exact modified chord-diagram rules, derive analytic expressions for uncrossed $2n$-point and crossed four-point functions, analyze their finite-temperature semiclassical and Schwarzian limits, study a deformation of the chord Hamiltonian that produces bound states and extends the correspondence with JT gravity plus an EOW brane to general brane tension, and identify an emergent $U(1)$ symmetry together with its finite-$N$ violation. Finally, we discuss analogies with boundary algebras proposed for black hole interiors and closed universes, and suggest lessons from our construction for both.

The Klein Paradox – the anomalous scattering of relativistic fermions off a high potential step – signals the limit of the single-particle interpretation of the Dirac equation. While Quantum Field Theory (QFT) resolves this via pair production, the microscopic mechanism is often obscured by abstract formalism. In this work, we investigate this phenomenon through the framework of Analog Gravity and Condensed Matter Physics. We utilize a hydrodynamic model wherein a relativistic particle is treated as a localized elastic excitation (defect) within a continuous linear medium. We demonstrate that when the external stress (potential) exceeds the medium's binding energy threshold ($V > 2mc^2$), the system undergoes a mechanical instability analogous to dielectric breakdown. This instability naturally generates modes with inverted topological winding, which we identify as antiparticles. By solving the boundary conditions for this elastic system, we reproduce the transmission coefficients of Hansen and Ravndal and recover the Schwinger limit for pair production rates. This approach provides a clear pedagogical model based on continuum mechanics to visualize vacuum decay processes, suggesting that the "paradox" is simply the elastic response of a medium under supercritical stress. This mechanical analogy serves as a pedagogical bridge for graduate students in condensed matter physics and advanced materials science, offering a concrete visualization of vacuum instability that complements standard abstract QFT derivations.

We present a theoretical analysis of the one-loop effective potential of a self-interacting real scalar field in the presence of two parallel conducting plates with geometric roughness. The analysis is restricted to the adiabatic regime of smoothly varying surface deformations, where derivative contributions to the surface profile can be neglected. Using Wentzel-Kramers-Brillouin methods to evaluate the spectral density of the modified Laplace-Beltrami operator, together with contour integration within a $\zeta$-function regularization scheme, we derive analytical expressions for the quantum corrections to the effective potential induced by perturbative boundary roughness and finite temperature. Furthermore, within this regime, we compute explicit contributions to the Casimir energy and to the topological mass generation associated with the geometry.

We derive the reduced Dirac Hamiltonian on the non-rotating BTZ background and use its redshift structure to construct a gauge-covariant single-band lattice model on the constant-time BTZ cylinder. In equal-area coordinates the AdS radius $L$ fixes the local Gaussian curvature, while the horizon radius $r_h$ fixes the throat size and the strength of the near-horizon redshift. The lattice model therefore has a direct geometric interpretation and is not presented as an unshown reduction of the two-component Dirac lattice. Its angular Fourier transform yields an exact curved Harper equation with BTZ-dependent hopping amplitudes and a consistent dimensionless angular quasi-momentum. We then supplement global parameter scans with state-resolved diagnostics: spectra color-coded by mean radius, local density of states, direct flux-response versus radius correlations, and Aharonov–Bohm spectral flow and persistent current on the BTZ cycle. These results show that weaker curvature sharpens the butterfly-like fragmentation, whereas larger horizons suppress both magnetic and Aharonov–Bohm response by creating weakly dispersing near-horizon states.

We investigate fermions on Carrollian manifolds. We complement previous intrinsic analysis by deriving Carrollian fermion actions from a relativistic Dirac theory via a systematic expansion in the speed of light ($c$). We then study relativistic fermions in light-cone coordinates and their connection to Carrollian fermions in one lower dimension. This follows from the recent observation that the Poincaré algebra, written in lightcone coordinates contains (two) co-dimension one Carroll sub-algebras. Our results establish a clear bridge between intrinsic Carrollian constructions, small $c$-expansion and light-cone dynamics. In the process, we understand why Carrollian fermions in $D$-dimensions have features that relate them to relativistic fermions in both $D$ and $(D+1)$ dimensions.

Unlike conventional charge-2e superconductors, a charge-4e superconductor exhibits long-range coherence of electron quartets rather than Cooper pairs. Clear zero-temperature realizations of charge-4e superconductivity remain rare. Here, we investigate the zero-temperature phase diagram of the attractive SU(4) Hubbard model with numerically exact, large-scale quantum Monte Carlo (QMC) simulations overcoming major technical hurdles. We identify both charge-2e and charge-4e superconducting phases. Upon increasing interaction, charge-2e correlations are suppressed and eventually vanish, while the charge-4e correlations remain robust and converge with system size, signaling the onset of a quartet-condensed phase. Interestingly, across the charge-2e–charge-4e transition, single electrons remain gapped, while charge-2e correlations exhibit a scaling behavior inconsistent with a conventional Landau description. These features are naturally captured by a fractionalized framework in which the physical charge-2e order parameter is a composite field coupled to an emergent non-Abelian gauge structure. We formulate an Sp(4) gauge-Higgs theory that realizes deconfined quantum pseudocriticality between the Higgs (charge-2e) phase and the confined (charge-4e) phase. The Sp(4) gauge-Higgs theory yields pseudocriticality through a fixed-point collision, and its one-loop collision-point exponents quantitatively track the QMC results. Our results establish charge-4e superconductivity as a bona fide zero-temperature phase, provide a simple model for future studies in a numerically exact framework, and reveal an unconventional route to superconducting criticality.

We consider Einstein gravity coupled to two Maxwell fields and one dilatonic scalar, and construct spherically-symmetric and static black holes that are charged under both Maxwell fields in general $D$ dimensions. We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. We devise a brute-force approach to obtain the most general but remarkably elegant solutions to the Toda equations. This allows us to construct exact black holes associated with all the rank-2 Lie groups. We study their thermodynamics and verify explicitly an earlier claim in the literature that all these thermodynamic quantities can be derived without having to solve for these black hole solutions.

Axion-like particles (ALPs), the QCD axion, and dark photons in the MeV-GeV mass range are motivated by various dark matter models and the strong CP problem, and are ubiquitous in extensions of the Standard Model. A long-standing blind spot for experimental searches is the sub-100 MeV mass range, where the particle lifetime is too long to be constrained by prompt-decay collider searches yet too short to be reached by beam-dump experiments. We investigate and estimate the sensitivity of the Light Dark Matter eXperiment (LDMX) to such axions and dark photons, motivated by the clean environment in which these particles can be produced and by the near-target tracking capabilities of LDMX. With reasonable charged track and momentum reconstruction capabilities, we find that LDMX could close much of this low-mass blind spot for axions and dark photons.

In the framework of Soft de Sitter Effective Theory (SdSET), the Fokker-Planck equation for the late-time dynamics of the massless minimally coupled scalar field and its extension to the Kramers-Moyal equation are obtained from operator mixing of composite operators of the effective superhorizon field. We construct the formalism for composite-operator renormalisation, mixing and matching in dimensional regularisation, allowing for computations beyond the leading order. The general formalism is illustrated in free SdSET, which already features non-trivial structures including the well-known diffusion coefficient for stochastic inflation. As explicit examples in the interacting theory, we renormalise the one-loop bispectrum and the two-loop one-point function of the composite operator $\varphi_+^2$, and match them onto their full-theory counterparts. These results allow us to determine the next-to-leading order (two-loop) correction to the diffusion term of the Fokker-Planck equation of stochastic inflation for the first time.

The path-integral approach to the double well has long been limited by the dilute instanton gas approximation. We show that if the finite Euclidean-time structure is taken seriously by using exact saddles, the dilute gas can be sidestepped, allowing the partition function and energy levels to be computed systematically. At each instanton order, the full resurgent structure – which saddles contribute, what asymptotic growth is expected and how ambiguities cancel – is encoded in a finite-dimensional Picard–Lefschetz contour integral over the quasi-zero modes with a clear geometric interpretation. Working at finite $T$ is essential: the dilute instanton gas can only access the ground-state splitting, whereas the exact finite-$T$ computation systematically produces the non-perturbative energy splittings for all excited states, including their full dependence on the level number. The key ingredients – Weierstrass elliptic functions for the saddles, Lamé operators for the fluctuations and Picard–Fuchs equations for the periods – form a coherent mathematical framework that both overlaps and complements that of Exact WKB.

Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states define a collection of quantum gates for a parallel quantum computation scheme that includes post-selection / projection as a gate. Structures such as gate complexity and more geometric complexity measures generalize to this setting. We provide a class of distance / distinguishability measures that extend the standard notion of distance for Lie groups to both continuous and discrete non-invertible symmetries, as well as more general linear combinations of unitary quantum gates. We illustrate these considerations by computing the distance between non-invertible symmetries in some 4D and 2D QFTs. We find that the simple objects of a symmetry category can be highly complex computationally.

We use the amplitude formulation of the SMEFT to introduce a spurion analysis of the SMEFT low-energy amplitudes in terms of the Higgs VEV. Each SMEFT contact-term is given as a sum of a few spurion structures, whose number depends on the electroweak charges of the external legs. The coefficients of these structures involve singlet combinations of Higgses from higher-order SMEFT contributions. We use this to derive the spurion expansions of the W- and Z-boson masses and mixing, and their three-point couplings to fermions. The textures of these couplings are saturated by the dimension-eight SMEFT. Our analysis can be generalized to higher-point amplitudes and nonzero Yukawa couplings.

Non-Clifford gates, used to generate quantum magic, are essential for universal quantum computation. We show that non-Clifford gates arise naturally from path integrals in topological quantum field theories, where their magic-generating properties are determined by the algebraic data of the theory. In Chern-Simons theory, we construct the Ising interaction gate, whose generator is prepared by path integration over simple three-boundary manifolds, and show that it produces non-local magic away from discrete Clifford points. We show that the Toffoli gate is obstructed in $SU(2)_1$ by the $\mathbb{Z}_2$ fusion structure, while $SU(2)_3$ is the minimal theory supporting the required conditional logic, given the density of the mapping class group in the projective unitary group on the manifold boundary. Finally, we demonstrate that the T gate arises as a path integral in Dijkgraaf-Witten theory, with gauge group $\mathbb{Z}_4$, where a single Dehn twist on the boundary torus produces the gate without approximation. These results show that topological path integrals construct gates in multiple levels of the Clifford hierarchy, and across distinct classes of field theories, with implications for topological quantum computing.

We compute the transmission properties of electromagnetic (EM), gravitational wave (GW), and static gravitational perturbations through geometric throats in spherically symmetric spacetimes. On the ultrastatic Ellis-Bronnikov background, decomposition of the four-dimensional Maxwell equations into vector spherical harmonics yields an effective Schrödinger problem with centrifugal barrier $V_\ell^{(\mathrm{EM})}=\ell(\ell+1)/(\sigma^2+r_0^2)$ peaked at the throat. For the lowest physical EM mode ($\ell=1$), frequencies below the barrier-top frequency $\omega_{\max}=\sqrt{2}/r_0$ are strongly suppressed by sub-barrier tunnelling. Gravitational wave perturbations ($\ell\ge 2$) see a qualitatively similar barrier and are likewise strongly suppressed below their respective barrier-top frequencies. By contrast, the static gravitational monopole ($\ell=0$), governed by the linearised Einstein equations on the same background, satisfies the source-free conservation law $(a^2\Phi')'=0$ with no potential barrier, yielding the exact solution $\Phi\propto\arctan(\sigma/r_0)$. We extend these results to a one-parameter family of throat geometries with varying profile shapes, and to a reflected-Schwarzschild (Damour-Solodukhin-type) wormhole, demonstrating that the qualitative asymmetry — strong sub-barrier suppression for all propagating radiation ($\ell\ge 1$) versus polynomial attenuation for the static monopole ($\ell=0$) — is universal for static, spherically symmetric throats. Numerov integration, WKB estimates, and exact analytical solutions are compared throughout. The results establish a structural constraint-wave asymmetry arising from the multipole decomposition of the field equations, independent of the matter content sourcing the geometry, on a fixed background.

We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem.

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete) time semicrystal phase emerges with persistent temporal order in disorder, bridging discrete time crystals and fully disordered regimes. This phase exhibits a periodic skeleton, with discrete subharmonic peaks persisting atop a continuous spectrum. We extract a critical scaling behavior across the discrete time crystal to time semicrystal transition. Furthermore, even dynamical transitions between distinct periodic skeletons can be clearly identified with systematic log-periodic corrections to power-law scaling, revealing discrete scale invariance. These findings in holography significantly enrich the platforms for studying nonequilibrium phases of matter.

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast C$ (respectively, the twisted cotangent bundles of $C$). Central to these constructions are Higgs bundles (respectively, holomorphic connections) which are transversal to line subbundles of the underlying bundles: these naturally induce divisors on $C$ together with auxiliary parameters, namely lifts to divisors on spectral curves for Higgs bundles and residue parameters of apparent singularities for holomorphic connections. We discuss the evidence showing that the Dolbeault geometric Langlands correspondence is generically realized by these Lagrangian correspondences; we expect that the de Rham geometric Langlands correspondence can be realized by their quantization, following Drinfeld's construction of Hecke eigensheaves. We also discuss the relations of our constructions to various topics, including reductions of Kapustin-Witten equations, the conformal limit, separation of variables, and degenerate fields in conformal field theories.

In the effective field theory (EFT) description of binary inspirals, the radiated gravitational waveform receives universal corrections from the curved background, the so-called “tail effects”, that resum into the so-called “Sommerfeld factor”. We develop a systematic framework for computing this gravitational Sommerfeld factor for scalar perturbations with the presence of tidal effects on the system. Using the worldline EFT, we recast the diagrammatic resummation as a solution to the $d$-dimensional wave equation with a localized source, and derive a closed-form expression for the Sommerfeld factor in terms of the EFT connection matrix. We prove that the phase of the Sommerfeld factor is exactly the same as elastic Compton scattering phase shift when there is no tidal dissipation. By combining the renormalization techniques in EFT with the Mano–Suzuki–Takasugi method in black hole perturbation theory, we analytically solve the Sommerfeld factor for both the magnitude and phase to $O(G^{10})$ for the $\ell = 0, 1, 2$ partial waves. We further establish a new renormalization group equation for the radiative multipole moments, whose exact solution yields an improved resummation of the waveform beyond the universal tail logarithms. These high-precision data and exact relations pave the way for future waveform resummation.