Papers

Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.

Renormalization group (RG) is a core concept in physics from statistical mechanics to quantum field theory, yet its schemes differ widely between field theory and many-body physics. We formulate the Wilsonian RG as a quantum channel, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension applicable beyond the usual momentum-space, factorized setting: the low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. We further construct a resource theory of RG whose free states are fixed points. For thermal states, the resulting relative-entropy monotone is proportional to $c-c_{\rm IR}$ to quadratic order along a single stable RG direction near a two-dimensional IR fixed point. We also introduce a complementary measure of the UV information discarded by coarse graining, establish its monotonicity for successive coarse-graining maps, and discuss its holographic realization.

The Yukawa-Sachdev-Ye-Kitaev (YSYK) model, a solvable model of non-Fermi liquids with a proposed cavity-QED realization, couples $N$ complex fermions to $M$ bosons of frequency $\omega_0$ through random Yukawa couplings of strength $g$, and its dynamics depends only on $R\equiv\omega_0/g^{2/3}$. For $R\ll1$ the bosons are slow and act as a static random background in which the fermions are free, while for $R\gg1$ they are only virtually excited and generate a random four-fermion interaction of rank $M$, which is generically chaotic for $M\geq2$. Using exact diagonalization at infinite temperature, we follow the emergence of random-matrix statistics between these limits with unfolded spectral statistics and the Krylov complexity of the thermofield-double state. For complex couplings the level-spacing distribution evolves from Poisson to Gaussian-unitary-ensemble (GUE) statistics, the spectral form factor develops a correlation hole and a ramp, and the Krylov complexity evaluated on the unfolded spectrum develops a peak above its late-time plateau whose height reaches the GUE value. All diagnostics locate the onset around $R\approx0.3$, and adding boson modes moves it to smaller $R$. This delineates the parameter regime in which a cavity-QED realization would display random-matrix spectral correlations. On the other hand, real couplings give the same crossover towards Gaussian-orthogonal-ensemble (GOE) statistics, and along an interpolation between the two the peak height follows the mean gap ratio, so the peak identifies the symmetry class as well as the onset of chaos. Without unfolding the peak stays about 20$\%$ below its random-matrix value in both classes, which we trace to the non-semicircular density of states, and at larger $R$ the boson-number bands slow down the spreading of the state in Krylov space.

In string model building, flavor symmetries can arise from the geometric features of the compactification space. In the case of heterotic orbifold models, modular and traditional flavor symmetries can be related to both geometric and algebraic properties of the orbifold space group. Our goal is to study the origin of moduli-independent discrete flavor symmetries in symmetric heterotic orbifolds with non-Abelian point groups. We develop various methods based on the Abelianization and the geometric automorphisms of the orbifold space group to determine these symmetries and their associated charges for matter fields. Notably, our methods were applied to all 331 non-Abelian affine geometries, including roto-translations, suitable for delivering N=1 supersymmetric heterotic compactifications in four dimensions. This provides additional motivation to pursue the derivation of new types of phenomenologically viable models from string theory.

Spontaneous scalarization of charged black holes in asymptotically flat spacetime has attracted much recent interest. It is recently reported that inside these spontaneously scalarized black holes, the Kasner parameter $\beta$ at the terminal singularity diverges as $\beta\propto(q/q_c-1)^{-\gamma}$ near the critical charge-to-mass ratio $q_c$, with an exponent $\gamma=1/2$ that appeared model independent within a wide class of couplings. In this paper we report a family of new universality classes in which $\gamma$ differs from 1/2. We show that all these critical behaviors are governed by the same emergent scaling symmetry at the would-be Cauchy horizon of the background Reissner-Nordström solution. This symmetry leads to a “seesaw amplification” to amplify exterior small scalar and produces a limiting autonomous system that is independent of the details of the theory. Our mechanism provides a unified picture of exterior scalarization and interior criticality and makes sharp numerical predictions that we test.

Could a collider become the symbol of everything that must be abandoned to save the climate? In the summer of 2026, this question ran through discussions within the Particles and Fields Division of the French Physical Society. An unacceptable carbon footprint, two EPR nuclear reactors, five hundred deaths, billions to be reallocated and, to top it all, unclear scientific objectives: the objections to CERN's Future Circular Collider (FCC) appeared to form an overwhelming indictment. This essay examines each charge in turn. Grounded in a clear and compelling scientific vision, it confronts emotionally charged imagery with orders of magnitude, distinguishes a project's footprint from its full balance sheet, considers the costs of postponing or abandoning it, and explores ways of reducing its impacts-including the still uncertain prospect of natural hydrogen. The climate alone does not decide the future of the FCC; it requires us to judge the available choices by their real consequences. Developed for the public debate organised by France's National Commission for Public Debate (CNDP) and for the Swiss consultation, this essay is intended for the broadest possible readership, well beyond particle physics and the scientific community. It frames the FCC debate as a choice about the kind of society we want to build: should we organise society around renunciation and ever-shrinking horizons, or transform how we produce and choose a future worth wanting?

Kehle and Unger have recently shown that self-gravitating charged classical scalar fields can collapse to form extremal Reissner-Nordström (eRN) black holes in finite time, thus violating the third law of thermodynamics (TLT). Reall has subsequently proved that the formation of an eRN black hole in gravitational collapse is impossible if the mass-to-charge ratio of the field exceeds unity, $m/e\geq1$. In the present compact paper we conjecture, using quantum considerations, that the Reall bound is not sharp. In particular, we point out that the electric field of a charged system with charge $Q$ will spontaneously polarize the vacuum in the regime $(eQ/\hbar)^2>(mQ/\hbar)^2+1/4$, thereby creating pairs of charged particles that discharge the black hole and ensure the quantum validity of the TLT in this regime. Motivated by the TLT, we conjecture that the classical Reall bound can be strengthened such that classical considerations would prevent eRN black holes from forming dynamically in the regime $m/e\geq\sqrt{1-\big({{\hbar}/{2eQ}}\big)^2}$, where quantum polarization effects are unable to protect the TLT.

Cosmological-collider signals are usually interpreted as clean probes of massive particles present during inflation. In this work, we study a massive spectator field excited by a spatially quenched random source, which may arise from a frozen realization of a light field or environmental sector whose relaxation time is long compared with the inflationary timescale. We determine which features of the collider signal remain reliable probes of the heavy field. After Gaussian disorder averaging, the random source modifies only the statistical component of the propagator, leaving the spectral function and heavy-field poles unchanged. The particle spectrum is therefore preserved, and the logarithmic frequency of the collider oscillations remains fixed by the heavy-field mass. What changes is how the massive modes are excited and imprinted on cosmological correlators: the temporal profile of the source controls the amplitude, phase, and envelope of the oscillations. For a power-law source, the fixed-realization problem is exactly solvable in terms of Lommel functions. Decaying sources can make the nonanalytic clock signal dominant in the squeezed limit, while spatial white noise can destructively interfere with the standard collapsed-trispectrum signal. Thus, mass measurements remain robust against this class of quenched disorder, whereas amplitude-based inferences can depend sensitively on the random environment.

We extend a previous study of the radial stability of solitonic boson stars by nonlinearly evolving them under aspherical perturbations, and by studying their formation from the collapse of scalar clouds. We focus in particular on models previously identified as radially stable, despite having positive binding energy, which ordinarily suggests that dispersion of all scalar matter is energetically preferred. A mode analysis of our 3+1 evolutions produces no evidence for the presence of a non-radial instability in any radially stable model, including those with positive binding energy. However, we do find evidence that such models do not generically form via gravitational cooling. We also find that it is possible to form another kind of compact object, which undergoes long-lasting radial oscillations and hence cannot be described as a stationary boson star. These objects may be characterized, we suggest, by energetically favoured multi-oscillating solutions to the Einstein-Klein-Gordon equations, present in certain regions of the parameter space.

We study the spinoptics equations for test electromagnetic wave in the Reissner-Nordström spacetime. The explicit and hidden symmetries of this background allow the complex null tetrad parallel-propagated along the null geodesic to be constructed explicitly. From this tetrad we obtain the evolution equations for the deviation of the ray from the null geodesic and for the tilting angle of its orbital plane. In these equations the charge term enters with a sign opposite to the mass term. Numerical integration confirms that the gravitational spin Hall effect becomes weaker with increasing charge: at a fixed impact parameter away from the critical value, the magnitude of the dimensionless tilting angle decreases with $Q$. As the turning point approaches the photon sphere, its magnitude grows firstly, and then exhibits an oscillatory behavior. Since the physical tilting angle is proportional to the reduced wavelength, it remains small whenever the spinoptics approximation is applicable. A divergence occurs only when the ray travels on the photon sphere.

We derive analytic response functions for Unruh–DeWitt detectors coupled to real, massless, conformally coupled scalar fields, to distinguish the effects of the field spectrum and global geometry from those of the interaction protocol. For Gaussian-switched static pairs in Minkowski, anti-de Sitter, and de Sitter spacetimes, we obtain the leading-order excitation probabilities and two-detector coherences in spacetime dimension $\mathcal D=d+1\ge3$. Time-ordered coherence requires distinct spatial worldlines; the local response and single-excitation coherence also admit coincidence. For equal-redshift pairs, Gaussian switching separates the gap dependence of the time-ordered coherence. In de Sitter space, KMS detailed balance fixes the gap that maximizes the ratio of nonlocal coherence to local excitation, giving a single-gap test for the existence of leading-order entanglement and restricting any entangling gaps to one bounded interval. When entanglement is present, the concurrence itself peaks at a smaller positive gap. In the three-dimensional BTZ black hole, an integrated Legendre series gives the sharply switched response of a radially infalling detector. A uniform image-sum estimate establishes logarithmic growth near the singularity and determines its coefficient from the covering-AdS response. A sufficiently smooth monotone onset removes the finite-time onset glitches but leaves a positive logarithmic coefficient; the accumulated leading-order response remains finite. Independent numerical calculations test the analytic expressions, their convergence properties, and these physical distinctions.

The observed cosmological constant is set by the deepest infrared scale of the present universe rather than by the microscopic scales that contribute to the vacuum energy. We show that this emerges as the quantum fluctuations of the gravitational field are progressively taken into account. Considering the Einstein-Hilbert+$R^2$ truncation of gravity, we find that in a wide region of the parameter space the theory develops instabilities that give rise to large amplitude quantum fluctuations which govern the renormalization group flow. Once the flow enters this region, it remains there all the way towards the infrared and progressively loses memory of its boundary conditions. The running cosmological constant $\Lambda_k$ ($k$ is the running scale) is driven towards the universal infrared scaling $\Lambda_k\sim \lambda_{_{\rm IR}}\,k^2$, with $\lambda_{_{\rm IR}}= \frac{1}{2(\pi-2)}$. At the deepest infrared scale $k_{_{\rm IR}}\sim H_0$ (the current Hubble scale), the cosmological constant is then screened to its observed value $\Lambda_{_{\rm IR}}\sim H_0^2$.

We study the Petrov classification and Weyl double copy of the four-dimensional bulk metric dual to a $2+1$-dimensional relativistic Rindler fluid at first order in the relativistic gradient expansion. Upon imposing the fluid equations, the leading Weyl curvature is determined by the fluid vorticity and shear. At this order, the bulk geometry is generically of Petrov type II, with a type D branch for shear-free flows with nonzero vorticity and a type N branch for irrotational flows with nonzero shear. For the type D branch, we construct a purely magnetic Maxwell single copy on a fixed Rindler background and distinguish exact source-free solutions with a constant magnetic field from local perturbative solutions valid through first order in gradients. For the type N branch, we obtain a family of algebraic Weyl double copies parametrized by $\beta$. We derive explicit field strengths and gauge potentials for $\beta=0$ and $\beta=1$, together with the local Cauchy-Riemann conditions imposed by Maxwell's equations. These choices encode the fluid shear differently: for $\beta=0$, the shear dependence resides entirely in the zeroth-copy scalar, whereas for $\beta=1$, it enters the Maxwell field directly. Finally, using the non-relativistic hydrodynamic expansion with explicit $\epsilon$ counting, we derive the non-relativistic limits of the type D single copy and both type N choices, and compare the resulting structures with existing non-relativistic constructions.

We establish uniqueness of the Veneziano four-point amplitude in a meromorphic class by combining six-point consistency with a known low-order supersymmetry relation. We consider planar tree-level scattering in four dimensions with a massless maximally supersymmetric vector multiplet and an additional scalar parity condition. A difference of supersymmetry Ward identities isolates massless factorization residues and eliminates every permitted contribution regular in a common kinematic limit. The resulting functional equation holds at every derivative order and fixes all angular dependence from the forward function after subtraction of the massless poles, at fixed Yang-Mills coupling. For a jointly meromorphic amplitude with simple planar poles, a nonempty spectrum of positive mass-squared poles separated from zero by a mass gap, nonnegative coefficients in the partial-wave expansions of scalar residues, and an exact unsubtracted forward dispersion relation, only the pole positions remain free. Positivity bounds their separation. The low-order relation saturates a sharp spectral inequality, requiring an infinite sequence of equally spaced mass-squared poles. The coupling and first massive pole position therefore determine the complete four-point function and all residues, without an initial finite-spin restriction.

Classical soft theorems govern the non-analytic structure of electromagnetic and gravitational radiation in the low-frequency regime, with the gravitational memory effect providing the canonical realization of the classical soft graviton theorem. While the soft behavior of radiation from hyperbolic scattering is well understood, its realization in gravitationally bound systems remains less explored. In this work, we study the soft structure of gravitational waveforms generated by compact binaries, focusing on the scattering of emitted radiation off the static background curvature within the multipolar post-Newtonian framework. We isolate the infrared (IR) logarithms associated with hereditary effects, including the tail-of-memory, and their higher generalizations with n-tail insertions. The resulting amplitudes exhibit a Laurent expansion in frequency space consistent with the Sahoo-Sen logarithmic soft theorems, thereby establishing a direct correspondence between gravitational memory effects, their higher-order tail corrections, and the soft expansion. We also comment on ultraviolet (UV) logarithms arising from short-distance sensitivity of the multipole expansion and their associated renormalization-group running.

We investigate 3d de Sitter axion wormhole which contribute to the no-boundary density matrix. We identify "cosmological necklace" solutions: an infinite series of Euclidean saddles corresponding with repeated bounces. This results in an unbound gravitational entropy, and a divergent path integral. To remedy this, we study the gravitational path integral using a (mostly) Lorentzian lapse contour. Within a minisuperspace steepest-descent analysis, we find that a single necklace dominates, leading to a finite entropy. A crucial element is to take into account an $(a\to -a)$ redundancy in the FLRW path integral, where $a$ is the scale factor. Surprisingly, the dominant solution is not purely Euclidean. Its entropy turns out to be independent of the axion flux, and equals the empty de Sitter entropy. We also study higher-dimensional necklaces, sourced by either an axion flux or by Yang-Mills instantons, and argue for qualitatively similar results: the single necklace solution dominates along a Lorentzian lapse contour.

The Method of Regions is a systematic way to derive asymptotic expansions of Feynman integrals. For Euclidean integrals there is a well-established algorithm to determine the complete set of regions as facets of a Newton polytope defined by the graph polynomials. In many physically relevant Minkowski limits, additional regions known as hidden regions are needed to obtain the correct asymptotic expansion. By making a precise connection with pinch singularities in parameter space and the associated Landau conditions, we identify the general mechanism giving rise to these regions and devise an algorithm, the Hidden Region Finder, to determine them. We show that hidden regions arise through a delicate interplay between asymptotic scaling of the edge parameters, which enhances certain monomials of the graph polynomial, and cancellations amongst these monomials, which reduce their collective contribution to the same order as other terms in the polynomial. We explore massless four-, five- and six-point integrals in a variety of wide-angle mass-shell, planar, collinear, double-collinear and Regge limits. Across these different expansions, hidden regions recur in the same small set of seed topologies. In all cases studied, they can be traced to wide-angle configurations with multiple hard-scattering subdiagrams. Distinct kinematic limits of a given seed inherit a common singular locus, while each limit fixes its own scaling vector and cancellation depth. This exploratory study showcases the potential of the proposed algorithm both to uncover missing contributions to asymptotic expansions and to organise them through their underlying singular geometry.

We present a new Plebanski formulation of General Relativity. The key difference is that we work with a gauge vector field derived from the Lanczos potential of the Weyl tensor. We show that, on shell, the gauge vector field encodes all nontrivial gravitational degrees of freedom and, in a suitable Lorentz gauge, Bianchi identities ensure that this gauge vector field satisfies a source-free wave equation for Ricci-flat spacetimes. This description suggests new ways of interpreting the true geometrical degrees of freedom with applications in both classical and quantum gravity.

We construct a smooth Riemannian metric with strictly positive sectional curvature on every smooth homotopy seven-sphere. For each smooth structure, we construct positively curved metrics on two seven-dimensional disks whose induced boundary metrics agree under the prescribed attaching map. Under this identification, a gluing theorem then yields the required smooth metric on the closed manifold. The construction applies to all 28 oriented diffeomorphism classes.

We present a compact all-multiplicity formula for tree-level late-time wavefunction coefficients of scalar QED in four-dimensional de Sitter space, with a conformally coupled charged scalar pair and positive-helicity photons. The result admits both a recursive representation in terms of shifted lower-point coefficients and an explicit finite sum involving only kinematic factors. The flat-space amplitudes vanish for two or more photons, yet the de Sitter coefficients remain nonzero. These zeros enforce cancellations of the total-energy residue and, through factorization, of proper partial-energy residues involving multi-photon subamplitudes. Using a common-reference construction, we derive an exact lower-point recursion from Abelian Ward identities. Conformal symmetry provides an independent check: the partition sum solves the inhomogeneous Ward identity, while the total-energy term is a homogeneous solution. We also outline an analogous recursion in massless fermionic QED.

We formulate the reduction technique for expanding the $n$-point AdS Feynman diagrams in two dimensions into the Wilson line networks. The technique applies to any $n$-point tree diagram, expressing it as several series of the matrix elements of Wilson line network operators, and employs the Wilson network expansions of the $(n-1)$-point AdS Feynman diagrams, which can in turn be obtained using the same technique. Consequently, the complexity of this technique does not increase with $n$, provided that the expansions of the $(n-1)$-point diagrams are known. To demonstrate the reduction technique, we apply it to all topologically distinct five-point AdS Feynman tree diagrams. The resulting expansions near the conformal boundary reproduce the known decompositions of the corresponding five-point Witten diagrams into conformal blocks.

We study large-overtone quasi-normal modes of a massive scalar field in a four-dimensional Schwarzschild de-Sitter black hole in the presence of a wall placed at the static sphere. Dirichlet boundary condition is imposed at the wall. At leading order the quasi-normal modes with large overtones scale as $n$ for $n\gg 1$ and are inversely proportional to the bouncing time. We analyze correction terms up to $n^{-1}$ order in the asymptotic expansion.

We develop an effective axi-Higgs model with one Standard Model Higgs doublet, one charged hidden Higgs and an anomalous Abelian vector portal. Extending previous Higgs–Stueckelberg constructions, we derive the Stueckelberg kinetic term by decoupling a heavy scalar radial mode and identify the gauge-invariant physical pseudoscalar from the mixing of the surviving scalar phases. A single instanton-motivated periodic interaction determines the axi-Higgs mass, its couplings to the hidden radial excitation and the sine-Gordon kink in the fixed-radial-field limit. We construct the anomaly-canceling gauge completion, using an Abelian A–B example to introduce the mechanism before its non-Abelian hidden-sector realization. We examine the relation between the periodic potential, the hidden gauge dynamics and the theta-vacuum energy, identifying the invariant angle through the anomalous Yukawa phase rotation. The vector portal gives a coherent elastic nuclear-scattering cross section and permits additional axi-Higgs emission, whose diagrams and kinematic threshold we determine. Numerical examples illustrate the mass and interaction scales, and we investigate conditional thermal relic abundances and their cosmological implications.

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

Chiral anomalies in baryon and lepton number currents in the GUT-inspired $SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification model in the Randall-Sundrum (RS) warped space are examined. Total anomalies including contributions of all Kaluza-Klein (KK) excited modes of fermions running along internal triangular loops are expressed in terms of the values of wave functions of gauge-boson KK towers at the ultraviolet (UV) and infrared (IR) branes in the RS space. The covariant divergence of 5D baryon number current picks up an anomaly term proportional to ${\rm Tr} \,F_{\mu\nu} \tilde F^{\mu\nu} |_{SU(2)_L} - {\rm Tr} \, F_{\mu\nu} \tilde F^{\mu\nu} |_{SU(2)_R}$ at the UV and IR branes where $SU(2)_L \times SU(2)_R$ is a subgroup of $SO(5)$.

Pulsar timing array (PTA) collaborations have reported evidence for a stochastic gravitational wave (GW) background in the nHz band. Should scalar-induced GWs, sourced at second order by enhanced primordial curvature perturbations, contribute to this signal, a coincidence of scales makes them directly sensitive to the softening of the equation of state around the QCD crossover. We solve the tensor and scalar equations of motion across the Standard Model (SM) thermal history and tabulate the transfer functions for direct use in present and future PTA analyses. We show that this SM effect modifies the height of the induced spectrum by up to $\approx55\%$ across the PTA band relative to the radiation-domination expectation, with either sign depending on whether the source modes cross the horizon before or after the crossover. Fitting the NANOGrav 15-year data with a broken-power-law curvature power spectrum, we find that including the crossover shifts the inferred peak amplitude and scale by an amount that could already be relevant for the comparison with primordial black hole overproduction bounds. The importance of this SM effect will grow as the statistical uncertainty on the amplitude and scale shrinks with future, more sensitive PTA datasets, at which point neglecting it could significantly bias the inference.

We construct an off-shell BRST-invariant gauge-fixed formulation of a nonlinear sigma model coupled to a non-Abelian gauge field. Starting from the dynamics of GBs and their consistent couplings to gauge and ghost fields, we construct the corresponding BRST-invariant quantum theory and provide a geometrical interpretation in terms of Killing vectors. A central point of our treatment is that the Lie-bracket closure of the target-space Killing vectors provides the geometric realization of the algebra entering the BRST differential. The physical state space is characterized by the cohomology of the nilpotent BRST charge, providing a consistent separation of physical and non-physical degrees of freedom. We explicitly derive the BRST charge and present the associated symmetry transformations. Finally, we analyze the structure of the physical Hilbert space and discuss the conditions under which BRST symmetry supports unitarity and constrains the quantum effective theory. Quantum statements are conditional on a BRST-preserving measure and regulator, and the four-dimensional model is treated as an effective field theory.

Minimal strings offer two ways to study quantum surfaces: through a spectral curve or through a differential equation. We ask how much of the quantum equation can be recovered once the classical curve and its motion with the background are known. Our starting point is the resolvent of a scalar differential operator. We require its one-boundary integral to have poles only at branch points, with the resulting differential regular at infinity. These conditions give a finite reconstruction procedure at each genus. When the branch points are simple and their energy values move, we prove that the quantum corrections are unique whenever the procedure is consistent. A specified string equation provides a solution if its trace primitive satisfies the same analytic conditions. The scalar construction also leads to amplitudes with several boundaries. We introduce the method through pure gravity and Ising, then explore higher-order, dual and nonunitary models. Higher-Airy examples connect the calculation to $r$-spin theory on a degenerate locus that requires a separate treatment of the inverse problem.

What happens to information carried through an evaporating black-hole horizon? We introduce a solvable model of evaporation built from coupled Sachdev-Ye-Kitaev systems, in which an initially two-sided black hole is coupled at a finite time to a larger, colder bath. Evaporation is rapid in this model, so we refer to the process as “blast freezing” of a black hole. In an appropriate large-$N$ and large-$p$ limit, the two-point functions and certain four-point probes can be computed analytically. Using the two-point functions as input to a generalized HKLL reconstruction, we obtain the emergent bulk geometry of the evaporation process. We then track the information carried by an infalling particle using operator size and Renyi-2 mutual information, showing how it is preserved in nonlocal many-body degrees of freedom after the blast-freezing transition.

We study how discrete parameters which enumerate non-crossing permutations become geometric quantities in JT gravity. Analyzing non-crossing permutations on the disk together with two classes of annular non-crossing permutations, we find that under suitable continuum scaling limits the number of marked boundary points becomes the thermal boundary length, while the number of through-connections becomes a geodesic length. In this limit, the enumerations reproduce the universal low-temperature behavior of the Schwarzian theory on the disk and the orientable and orientation-reversing double-trumpet geometries. We then relate these constructions to higher-boundary non-crossing diagrams, whose continuum enumeration reproduces the JT result obtained by attaching trumpets to the top-degree part of genus-zero Weil-Petersson volumes, suggesting that the same trumpet–enumeration parameter mapping extends beyond the planar case. Together, these results establish a direct connection between non-crossing permutation enumerations and Weil-Petersson volumes with trumpets attached, a construction that plays a central role in the gravitational path integral in JT gravity, and suggest that non-crossing diagrams provide a combinatorial route to computing multi-boundary partition functions.