Papers

Solving the strong CP problem with spontaneous CP violation (SCPV) in SUSY requires that the constant term of the superpotential and the SUSY-breaking F-term be real to high accuracy. When both are generated dynamically, by gaugino condensation and by dynamical SUSY breaking (DSB), their phases need not vanish even if every theta-angle vanishes and every coupling is real; e.g., the multivalued non-perturbative superpotential may sit on a branch with a complex phase. In fact, gaugino condensation, in pure SUSY Yang-Mills theory and in its Affleck-Dine-Seiberg generalization, is safe only for N_c - N_f in {1,2} (N_c = 2 for pure SYM); otherwise the phase of the constant term reaches the gluino mass through anomaly mediation. The SUSY-breaking F-term is the main source of the MSSM soft masses, including the gluino mass, so its phase reaches theta-bar as well. In the framework of global SUSY, the 3-2 model introduces no phase. The ISS model is safe in that sector as long as the quark-mass splittings exceed the messenger-loop corrections; when they fall below, a complex vacuum orientation can generate an O(1) phase. The IYIT model can generate a purely imaginary F-term: for half of the real Yukawa parameter space, the meson VEV is purely imaginary and CP is spontaneously broken. In all three, the vacuum of the field coupled to the messengers is aligned with the constant term, so a complex constant term generates a strong CP phase through a second route, separate from anomaly mediation.

Stochastic bubble nucleation makes the local completion time of a first-order phase transition a random spatial field. We study its power spectrum and equilateral bispectrum in Minkowski and de Sitter backgrounds, with particular emphasis on the infrared consequences of a finite transition duration. In an eternally extended de Sitter history, rare bubbles nucleated in the remote past generate an ancient-bubble tail that produces a hierarchy of infrared-sensitive spatial moments. For the two-point function, the first finite-$k$ correction becomes tail sensitive at $H/\beta=1/5$, while the leading moment becomes singular at $H/\beta=1/3$. The corresponding three-point thresholds are $H/\beta=1/8$ and $1/6$, showing that the bispectrum is more infrared sensitive than the power spectrum. For any finite starting time, however, the ancient-bubble tail is cut off, all spatial moments remain finite, and the strict infrared spectra recover the analytic white-noise limits ${\cal P}_\tau\propto k^3$ and ${\cal B}^{\rm eq}_\tau\propto k^6$. The eternal-background thresholds instead control the duration dependence of the moment coefficients and the crossover into an intermediate tail-sensitive regime, in agreement with our numerical calculations. We further show that temporal localization of the nucleation history provides a smooth regulator of the ancient-bubble tail and restores the same analytic infrared limits. These results establish a general first-arrival framework for completion-time fluctuations and clarify how de Sitter expansion can generate distinct power-spectrum and bispectrum infrared hierarchies relevant to curvature perturbations and non-Gaussianity.

Recently, Cotler, Ivo, and Maldacena have shown that under scale invariance, eternal inflation is interpreted as a failure of the reheating surface volume renormalization due to an ill-defined scaling dimension. Meanwhile, observations suggest that scale invariance is slightly broken, which is parametrized by deviation of the spectral index from unity, $\varepsilon=n_s-1$. Motivated by this, we study how the scale invariance breaking effect modifies the no-eternal inflation condition as the renormalizability of the reheating surface volume. For this purpose, we adopt two independent approaches: investigating the behavior of the normal ordered reheating surface volume operator under a shift of the curvature perturbation, and analyzing the coarse-graining structure to obtain the scaling dimension. Both approaches commonly reveal that as long as $\varepsilon$ is negative, which is consistent with observations, the fractal structure of the reheating surface volume breaks down at macroscopic scale, moderating the no-eternal inflation condition.

We show that Hawking radiation spontaneously generated by dynamical black-hole formation can be realized in a local quantum spin model. Starting from the ground state corresponding to the early-time vacuum, with no initially prepared excitations, we follow the dynamics induced by the evolving geometry. In the corresponding continuum quantum field theory, Hawking particle creation is associated with nontrivial Bogoliubov mixing between the in- and out-mode decompositions. We derive the resulting renormalized local energy density in the continuum quantum field theory, which corresponds to an energy-weighted integral of the Hawking spectrum, and identify its counterpart as a local spin observable whose expectation value quantitatively reproduces the continuum prediction, including its dependence on the surface gravity. The agreement persists over a finite time window whose duration grows logarithmically with system size, revealing the crossover from universal continuum Hawking physics to lattice-cutoff dynamics. These results establish a microscopic route to quantum simulation of quantum field theory in curved spacetime, connecting field-theoretic particle creation directly to experimentally accessible many-body observables.

We show that in hot QCD rotating at an imaginary angular velocity $\Omega_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $\theta$, with $\Omega_I/2\pi=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $\theta'=q\theta+\pi(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature. The bulks at $\Omega_I=2\pi/3$ and $4\pi/3$, for example, are both at temperature $T/3$, yet only the former can break $C$. The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $\Omega_I/2\pi$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.

We construct a magnetic soliton by double Wick rotating the static electrically charged black hole in three-dimensional Einstein–Gauss–Bonnet gravity. We match the boundary metrics and Maxwell sources under the chosen boundary condition and compute the difference of the renormalized Euclidean actions. Because the Maxwell potential grows logarithmically at infinity, the chosen finite Maxwell boundary term changes both the fixed Maxwell source and the renormalized action. The charge contributions for both the soliton and the black hole appear with plus signs in $\Delta I^{(c_{\mathrm{fin}})}$. For the grand-canonical boundary condition $c_{\mathrm{fin}}=1$, the black-hole and soliton branches can cross with different slopes. For the example considered below, the black-hole branch satisfying the response conditions ends at a maximum temperature, and the coexistence curve has a $T\to0^+$ endpoint at two opposite values of the spatial Maxwell source. At a nonextremal crossing, the entropy difference is $S_b-S_s=S_b$. For these two static solutions, equality of both current components requires both charges to vanish.

We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature $T_D=1/(\pi\alpha)$, where $2\alpha$ is the temporal extent of the diamond. The regulated Gibbons–Hawking–York contribution gives $I_D^E=-A_0/(4G)$, with $A_0$ the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy–area relation $S_D=A_0/(4G)$. For weak matter perturbations crossing a localized portion of the future horizon, a Raychaudhuri analysis relates the associated Killing-energy flux to the area response, yielding a local physical-process first law at leading order near the bifurcation surface and, for classical matter satisfying the null energy condition, a local second law. Uniform conformal surface gravity establishes the zeroth law, while zero temperature is approached only in the limit $\alpha\to\infty$, in which the finite causal horizon disappears. These results show that a coherent horizon-law structure can arise within a causal diamond, a fundamental building block of the causal structure of Minkowski spacetime. The derivation is explicit in $(2+1)$ dimensions, while the physical results retain the same form for spherical causal diamonds in $d\geq3$.

A fermion mass pairs a field with a partner of conjugate charge: elementary (Higgs-Dirac), self-conjugate (seesaw) or a three-fermion composite (symmetric mass generation, SMG). We give half of a Spin(10)-like generation an explicit Majorana mass in a four-dimensional SMG model and ask what the other half does in a phase with no condensate. With the source on, every mass-type term of the unsourced half averages to zero under the symmetry group of the sourced action, so a light mass term, and a seesaw's light-heavy mixing, requires a spontaneously broken symmetry; exact on the lattice and a general proposition. The source is colour-democratic (a Delta_R-type mass on every flavour's right-handed taste doublet); the single-nu_R split lies outside the positivity class used but inside the symmetry statement. Measured up to 8^4: (i) in the symmetric-gap phase, with the source screened to at most 1.1% of free, the unsourced half's single-fermion readout stays at 0.3% of free while its pair susceptibility rises from 0.2% to 1.2-1.7% at h=2; on like mode sets it falls with the volume, on (4^4,8^4) no inequivalent light mass channel grows faster than free, and symmetry breaking is not resolved at L<=8; (ii) at the critical point the explicit mass collapses the critical sigma channel and moves the light half toward free as a saturating crossover, not a power law; direction tests (MIXED by their pre-registered letter) are consistent with a critical coupling rising with the mass; y_c(h) is not located. Pole versus zero of the light propagator at p->0 is not measured. The outcomes are readings after pre-registered tests that mostly returned no verdict. Also: no first-order signature of the merged transition at L<=8, a Z_4-odd response handed to a lattice composite, and flavour democracy of the positivity class. Every claim has an evidence class and a runnable check.

We construct the bulk local states of a massive spin-1 field in AdS$_3$/CFT$_2$ and three-dimensional Carrollian holography. In AdS, covariance under the isometries that leave a bulk point invariant determines the three components of the vector there and splits the solution into two branches of definite helicity, whose inner products reproduce the massive vector two-point function of AdS$_3$. By expanding the massive vector HKLL representation in boundary descendants, one can reproduce the three component states term by term. The two branches together describe the parity-invariant Proca field, and one alone the single propagating mode of Maxwell–Chern–Simons theory. The same conditions are solved in the induced representation of the Carrollian theory, where the solution again splits into two branches. Under the flat limit of the generators the highest weight module becomes the induced module, and the AdS states and Green's functions become their Carrollian counterparts, which supports the induced representation as the home of massive bulk excitations in Carrollian holography. This is the first bulk local state built with spin, complete from the state itself to its bulk-to-bulk propagator and to the limit relating the two descriptions.

Extending the Fokker–Planck equation to a coupled system of equations through non-Abelian symmetry groups offers a powerful theoretical framework for coupled multi-state stochastic systems. However, translating this abstract gauge field formulation into viable numerical predictions remains an unaddressed challenge. Motivated by our previous work on ice crystal habit evolution, in this work we bridge this gap by presenting the first numerical solver for an SU(2) gauge-coupled Fokker–Planck system in (1+1) dimensions. Using an operator-splitting scheme combined with a non-oscillatory advection solver, our algorithm strictly ensures probability conservation, non-negativity, and numerical stability. We demonstrate that non-Abelian gauge coupling acts as a cross-reactive feedback loop that fundamentally alters system dynamics, driving continuous probability exchange between states, suppressing localised density peaks, and forcing long-time spatial delocalisation. Validated across linear and quadratic coupling regimes up to strong interactions (g <= 1.0), this work establishes the foundational computational infrastructure needed to integrate complex multi-state physics. Overall, while our approach provides a key step toward improving ice cloud representation in atmospheric and climate models, the underlying physical framework and computational engine remain fundamentally general and multidisciplinary, offering a versatile paradigm for any domain requiring coupled multi-state stochastic equations.

In this thesis we study the high-energy and collinear behaviour of gravitational scattering amplitudes and their relation to classical scattering and radiation observables. Multi-Regge kinematics, characterised by a strong rapidity ordering, provides the factorised building blocks governing the leading logarithmic structure. Relaxing this ordering to next-to-multi-Regge kinematics allows two neighbouring particles to have comparable rapidities and provides the real emission building blocks entering at next-to-leading logarithmic accuracy. We extract the next-to-multi-Regge impact factor from tree-level MHV amplitudes for pure gravitons and derive its gravitational splitting functions. We then use BCFW recursion relations to reconstruct the five-point tree amplitude for two massive scalars scattering with the emission of one graviton. Its high-energy limit yields the massive scalar–graviton impact factor and, through the KMOC formalism, a representation of the leading high-energy collinear waveform. Finally, by sewing the relevant vertices across unitarity cuts, we construct the elastic \(H\) kernel, its radiative extension and a classical next-to-multi-Regge kernel. The latter reproduces the standard \(H\) kernel in the multi-Regge limit and the universal Weinberg current in the soft limit.

We study Maxwell theory near a nonextremal bifurcate Killing horizon in a general static, spherically symmetric spacetime of dimension $D>3$. We impose near-horizon boundary conditions in a regular Eddington–Finkelstein chart that retain both radiative and Coulombic data, and construct the associated horizon phase space and large-$U(1)$ charge. At null infinity, the radiative falloff depends on the spacetime dimension and involves half-integer powers in odd $D$, whereas a nonextremal horizon at finite radius supports radiative data with an ordinary integer-power expansion. Expanding the horizon fields in Killing frequency and spherical harmonics, we derive the associated soft-photon relation from the large-$U(1)$ Ward identity. For comparison, we express the flat-space leading soft-photon theorem using the same spherical harmonics and commutator normalization as the horizon modes. In $D=4$, the two relations have the same soft-frequency dependence and the same angular dependence of the hard-charge terms, whereas for $D>4$ the flat-space relation contains additional dimension-dependent frequency and angular factors.

We study quantum algorithms for finding a vacuum with a small cosmological constant in the toy model for string Landscape proposed by Arkani-Hamed, Dimopoulos, and Kachru. First, we construct a function-value oracle and use it for Grover search with query complexity $\mathcal{O}(2^{N/2})$, where $N$ is the number of scalar fields. Then, we point out that, by exploiting the linearity of the vacuum energy, the problem can be reduced to a collision problem between two blocks of the bit string. With this structure, we construct two quantum algorithms with query complexity $\mathcal{O}(2^{N/3})$. Compared with the pseudo-polynomial classical algorithm of Denef and Douglas, the quantum algorithms yield a large reduction in computational cost for the physically motivated parameter values.

We study the magnetic-field-driven critical end point (CEP) of the QCD thermal transition at zero baryon chemical potential using a five-dimensional Einstein–Maxwell–dilaton (EMD) model. We calibrate the model to lattice entropy at zero and finite magnetic fields using a neural-network formulation of holographic radial evolution. As the magnetic field increases, the thermal transition changes from a crossover to a first-order transition. The merger of temperature turning points, a divergent specific heat, and a vanishing squared sound speed identify $(eB_c,T_c)\simeq(7.22\,\mathrm{GeV}^{2},95.9\,\mathrm{MeV})$. The transition-region inflection of $s/T^3$ defines the crossover temperature, while an equal-pressure Maxwell construction determines the first-order coexistence line. The two lines meet at the CEP. The change of transition order agrees qualitatively with lattice results. The phase boundary is a prediction of the calibrated model.

We study a representative two-loop family of worldline quantum field theory integrals relevant for classical gravitational scattering with a massive mediator and investigate the geometric structure of its maximal cut. We find that, unlike the massless case, the massive loops already give rise to an elliptic maximal cut at two loops, which degenerates into a nodal curve in the massless limit and in the static limit. In the global Baikov representation, two successive integrations reduce the maximal cut to a period of an elliptic curve. We further establish five primary consequences of this study: (a) The integration-by-parts method generates five master integrals, which, under reflection, split into a three-dimensional elliptic block and a two-dimensional polylog block. We derive the differential equation in two ways, one by Laporta reduction and subsequently by intersection theory in two cocycle bases, and construct the rational map between them. (b) The period matrices in arbitrary dimension have been computed in terms of Appell and Beta functions. Furthermore, we derive twisted Riemann period relations that yield nine quadratic identities among them. (c) We study the global monodromy relation of the differential system that satisfies Riemann's bilinear relation. (d) We explicitly derive the function space of the iterated integrals in terms of elliptic multiple polylogs. (e) In impact-parameter space, the Fourier-transformed cut is a Bessel-twisted differential on the elliptic curve, which we show has extra involution symmetries. Thus, the parity of the differential further decides which quotient - rational or elliptic its periods live on. All results presented concern the maximal cut and, therefore, the homogeneous solutions, but they open an important pathway to tackling the full massive two-loop integral.

We integrate the Bondi–Sachs hierarchy of scalar–Gauss–Bonnet gravity with an arbitrary coupling function $f(\Phi)$ and a radiating massless scalar, and determine the first order in $1/r$ at which the coupling $\lambda$ becomes visible in each field equation. We obtain the asymptotic falloff of the effective Gauss–Bonnet stress tensor together with its leading coefficients in covariant form on the sphere: every component decays between one and three powers of $1/r$ faster than the slowest falloff compatible with a smooth null infinity. As a consequence, (i) the Bondi mass-loss formula and the evolution equation of the angular-momentum aspect are those of the minimally coupled Einstein–scalar system, a statement that is exact in $\lambda$ under the assumption of a smooth expansion; (ii) the coupling generates no logarithmic terms through the orders considered, even though the Horndeski representation of the theory involves logarithmic functionals; and (iii) the coupling first enters a dynamical equation in the evolution of the $O(r^{-3})$ coefficient of the angular metric, through the cross term $-2\lambda f'(\vp_0)\,\vp_1\,\partial_u N_{AB}$ between the asymptotic scalar charge aspect and the time derivative of the news. In Newman–Penrose form, the evolution equation of the leading coefficient of $\Psi_0$ acquires the source $-12\lambda f'(\vp_0)\,\vp_1\bar\Psi_4^0$, while those of $\Psi_1$ and $\Psi_2$ are unchanged. The Gauss–Bonnet invariant decays as $r^{-6}$ and affects the scalar hierarchy only from the evolution of the $r^{-5}$ coefficient onward. For vacuum black-hole spacetimes, where the scalar is sourced by the coupling itself, all these effects are of order $\lambda^2$; if $f'(\vp_0)=0$ they are pushed one further order in $1/r$.

Generalized entanglement wedges (GWs), proposed by Bousso and Penington for gravitating regions in general spacetimes, share many properties of ordinary entanglement wedges, including nesting, monotonicity and strong subadditivity of their generalized entropies. In AdS/CFT, the corresponding properties of entanglement wedges are consequences of the structure of the dual CFT. In this paper we ask whether the properties of GWs have a similar origin. We explore this question in vacuum AdS$_3$ at leading order in $G$. We first show that every GW on a static slice is a union of geodesically convex regions. Each such region is an intersection of ordinary entanglement wedges, so every GW is built from unions and intersections of entanglement wedges. We then use the Crofton formula of integral geometry to write the perimeter of a convex region as the measure of the set of geodesics that intersect it. In AdS$_3$ every geodesic is the Ryu–Takayanagi surface of a boundary interval, so this measure can be written in terms of the von Neumann entropies of CFT intervals. Strong subadditivity of the CFT entropy guarantees that the measure is positive. Monotonicity and strong subadditivity of GWs then follow from simple inequalities between sets of geodesics. The strong subadditivity of GWs is therefore a direct consequence of strong subadditivity on the boundary. Our results further suggest that GWs correspond to subsystems of the CFT that are more general than boundary subregions.

In this work, we revisit the analytical structure of the classical affine Lie bialgebra underlying the integrable structures of AdS/CFT worldsheet scattering and the one-dimensional Hubbard model. Earlier work showed that the algebraic relations implied two singularity locations in the evaluation parameter plane besides the common expansion points infinity and zero for Laurent polynomials forming the basis for loop and affine algebras. Our aim is to formulate these singularities rigorously using meromorphic functions rather than by expansion into geometric series. We thus carefully analyse the analytical structure of the affine bialgebra relations in the complex plane paying attention to potential restrictions and extensions due to the additional singularities. As a first attempt with some shortcomings, we reformulate the affine bialgebra relations with the extra singularities serving as the expansion points for Laurent polynomials. We finally overcome the remaining issues by proposing three-point and four-point affine algebras for the rational and trigonometric cases. With a suitable choice of basis for meromorphic functions on the Riemann sphere with several punctures based on Krichever-Novikov algebras, we show that the multi-point affine algebras form consistent quasi-triangular Lie bialgebras.

We study scalar collapse in five- and six-dimensional Einstein–Gauss–Bonnet gravity with positive coupling, treated as an exact classical theory. On spherical scalar backgrounds, the characteristic conditions of the tensor, vector and scalar gravitational sectors reduce to inequalities in two local invariants: $K=1+\tilde\alpha F/R^2$, which compares the enclosed mass with the areal radius $R$, and a scalar-gradient invariant $j$. In five dimensions they imply $R_h^2>\tilde\alpha$ for the areal radius $R_h$ of a regular marginal sphere on the GR branch and the sharp bound $\tilde\alpha^2\mathcal R_{abcd}\mathcal R^{abcd}<28$ for nonnegative mass. For initially untrapped five-dimensional spherical data with a regular center, a bound on $K$ alone ensures smooth continuation on compact domains of dependence, so any first characteristic loss occurs on a smooth background, and a marginal sphere formed before any loss forces a later loss. Complete smooth data form marginal spheres at every allowed radius with mass arbitrarily close to its sharp lower bound; in six dimensions radius and mass can both be arbitrarily small. Without spherical symmetry, complete initial data with weak curvature contain, at sufficiently large scale, outermost strictly stable marginal surfaces with prescribed $S^3$ geometries satisfying a spectral condition; Berger surfaces among them have arbitrarily small area at fixed mass. Their formation from untrapped data is left open. Near a contracting homogeneous core, exact nonspherical developments of smooth constrained data converging with every derivative have bounded curvature but, after the core's characteristic loss, a fixed discrepancy in a geometric tidal record. Classical existence, local geometric uniqueness and continuity of this pointwise record cannot all be guaranteed on a common observation region. A companion paper treats narrow incoming pulses.

In a (1+1)-dimensional QFT with non-invertible symmetry, the fusion rules of topological lines are often the most accessible data, yet they do not fully determine whether the symmetry is anomaly-free, i.e. whether it admits trivially gapped phases. Such phases are characterized by fiber functors of the corresponding fusion category. Building on Tannaka duality, we extract fiber functors from the fusion ring alone by solving simultaneously for monoidal structure maps and tensor automorphisms. This allows us to find categorifications admitting a fiber functor without solving the pentagon equations directly. We test this procedure on the known Tambara–Yamagami ring of $\mathbb{Z}_2\times\mathbb{Z}_2$. Our main result concerns the rank-11 fusion ring shared by the representation categories of the two extraspecial groups of order 27, which has a multiplicity 3 channel and is relevant to self-triality. In both cases we find more than one fiber functor, i.e. several non-invertible SPT phases. We use the explicit data of these fiber functors to derive the $F$-symbols of the two representation categories in a compact form depending on a non-degenerate alternating bicharacter and an invertible object $\epsilon$. Using the reconstructed data, we compute the anomalous algebra on the interface between two different SPT phases.

Interpreting neutrino oscillation measurements requires computing the probability that a neutrino born with one flavor is detected with another. In vacuum and in matter of constant density, this probability has exact formulas. Where the density varies along the path, as in the Earth, the Sun, or a supernova, it does not. There, the usual approaches either replace the profile by constant-density steps, whose error falls only as the square of their width, or integrate the evolution equation with a general-purpose solver, which must shorten its steps to meet a tighter tolerance. Both become slow at high accuracy, yet an analysis needs the probability at many energies, directions, and parameter values. Each new experiment or model often requires writing and validating a new solver. We present Magnus, an open-source Python code that avoids these limitations. It uses the Magnus expansion, whose error falls as a high power of its step width and whose cost is set by how fast the density varies, not by how many oscillations the path holds. Magnus accepts any density profile, any number of flavors, and any Hermitian Hamiltonian, such as those of non-standard interactions, sterile neutrinos, Lorentz-invariance violation, and pseudo-Dirac neutrinos. Where a cheaper route exists, it takes it automatically. For example, where the density varies slowly, as in the Sun, it follows the instantaneous eigenstates and applies the expansion only at resonances. Besides oscillating probabilities, Magnus returns phase-averaged ones, which describe solar and astrophysical neutrinos. A typical probability takes a few milliseconds, and batched scans are one to two orders of magnitude cheaper per point. Among the public codes we compared, Magnus is the fastest at high accuracy on a varying profile. Magnus shifts the effort of studying a new experiment or model from writing a solver to specifying its physics.

We study magnets composed of molecules with atoms interacting via $SU(N)$-invariant two-body interactions. Atoms carry states transforming in generically different irreducible representations of $SU(N)$, and the interaction strength between atoms depends on the specific atoms involved. We derive the thermodynamics of these magnets in the mean-field approach, and find that they can exhibit mixed ferro-antiferromagnetic behavior. We present a full analysis of the simplest nontrivial case of molecules consisting of two atoms in the spin-$j$ representation of $SU(2)$, which generalizes conventional magnetic systems, and derive its phase structure and transitions.

Although the spontaneous decay of axions into two photons is extremely slow on cosmological timescales, it can be strongly enhanced in environments with large bosonic occupation numbers. From a classical field perspective, stimulated axion decay is described by modified Maxwell equations. For a coherent axion background, these equations exhibit a parametric resonance characterized by a photon growth exponent $s\propto g_{a\gamma}$. By contrast, a standard kinetic description, for instance based on Boltzmann equations, involves the squared matrix element of the decay process and therefore would naturally predict a characteristic rate scaling as $s\propto g_{a\gamma}^2$. In this work, we show that these apparently different behaviors originate from the coherence properties of the axion field. Starting from an axion field with a finite momentum dispersion, we show how dephasing among its momentum modes modifies the photon instability and derive an effective evolution equation in which this effect is encoded in a kernel. For a continuous Maxwell-Boltzmann distribution of axion velocities, we obtain an implicit expression for the photon growth exponent that reproduces the two asymptotic regimes and provides an approximate description of the crossover. When amplification develops on scales shorter than the axion coherence length, the parametric resonance scaling $s\propto g_{a\gamma}$ is recovered, whereas in the opposite limit an effectively kinetic behavior with $s\propto g_{a\gamma}^2$ emerges. Although the detailed form of the crossover depends on the axion momentum distribution, we expect the asymptotic scaling with $g_{a\gamma}$ to be largely insensitive to the specific distribution assumed.

String Theory provides powerful tools for constructing and studying five-dimensional Quantum Field Theories, notably through geometric engineering and five-brane webs. Understanding how these two descriptions are related in the presence of 7-branes requires incorporating the s-rule into the geometry. To address this question, we focus on basic three-legged five-brane webs ending on 7-branes. Building on the local M-theory description of five-branes ending on 7-branes, we consider triangular toric diagrams with a single non-primitive edge. We show that the corresponding local complex-structure deformation is well defined on the overlaps with the neighboring toric patches, while the corresponding gluing map remains well behaved as a function of the holomorphic coordinates throughout the neighboring patches precisely when the s-rule is satisfied. At saturation, the geometry is a T-cone and the 7-brane deformation becomes its Q-Gorenstein smoothing. Our results thus identify the s-rule with the obstruction to globalizing the local 7-brane deformation and provide a direct geometric link between T-cones and five-branes ending on 7-branes.

We apply equivariant localization to supersymmetric $AdS_3\times M_8$ solutions of eleven-dimensional supergravity, dual to two-dimensional $\mathcal N=(2,0)$ SCFTs. We construct equivariantly closed polyforms encoding the magnetic flux and its dual, calibrated M2-branes and the warped volume, reducing protected observables to fixed point data of the $U(1)$ R-symmetry action. We apply the framework to $S^4$ bundles over coassociative four-cycles and $S^2$ bundles over compact six-manifolds, obtaining topological formulae for leading central charges and gravitational anomalies in terms of quantized fluxes and topological data. We recover the known results for $T^2\times KE_4$ solutions and construct a compact numerical solution with quantized flux that lies outside the known polynomial branch.

We study the generalized symmetries associated with Standard Model flavor and their fate in the presence of magnetic monopoles. This illuminates a striking phenomenological consequence: even when baryon and lepton number are classically conserved, the electroweak anomaly induces $\Delta B = \Delta L \in 3 \mathbb{Z}$ in monopole-fermion scattering for any monopole activating the anomaly. We demonstrate this mechanism in Pati-Salam theory and trinification.

We complete the systematic derivation of the Quantum Spectral Curve (QSC) for strings on $\text{AdS}_3\times\text{S}^3\times \text{T}^4$ with pure Ramond–Ramond (RR) flux, building on the extended Y-system obtained in our preceding paper. We establish the precise relation between the two formalisms of the Thermodynamic Bethe Ansatz and the QSC, derive the previously conjectured QSC, and, along the way, uncover additional relations satisfied by its solutions. Our analysis also clarifies how massless excitations, although not explicit among the basic QSC building blocks, are encoded in their analytic structure. The derivation culminates in the so-called $\mathbf{P}{\mu}$-system, a compact formulation of the QSC in terms of a small set of functions and their analytic continuations.

The back-to-back limit of the energy-energy correlator (EEC) exhibits a finite plateau, capturing the evolution from perturbative soft-collinear radiation at weak coupling to string dynamics at strong coupling. At weak coupling, we resum its leading and next-to-leading-power logarithms through N$^3$LL in $\mathcal N=4$ SYM, including non-planar contributions. Combining this weak-coupling endpoint with bootstrap and strong-coupling data, we construct an interpolation for the plateau height from weak to strong coupling. The calculation uses a human-in-the-loop agentic workflow.

We compute Kerr-Newman quasinormal modes using a recently found exact separation of the gravitoelectric perturbation equations. For each spin-label $\varsigma=\pm1$, a matrix angular ordinary differential equation and a scalar second-order radial ordinary differential equation define a joint spectral problem for the complex frequency $\omega$ and separation constant $\lambda$. We solve this problem by imposing regularity at the angular poles, ingoing behavior at the event horizon, and outgoing behavior at infinity. We benchmark the numerical code built to solve the separated equations, and the resulting frequencies, against recently published spectral calculations of the coupled system. Comparisons with those results yield absolute differences of order $10^{-10}$ to $10^{-5}$, depending on the BH parameters and overtone number. We also find numerical hints of spin-label isospectrality in both the electromagnetic-led and gravitational-led sectors of fundamental quasinormal modes, even at near-extremal Kerr-Newman configurations. These results provide numerical evidence that the separated equations reproduce Kerr-Newman quasinormal frequencies and offer a practical route to exploring the ringdown of rotating, charged black holes.

We test the proposed matrix-tensor description of three-dimensional gravity using a Schwinger-Dyson relation in its purely open sector. We enumerate and classify the topological contributions to a cylinder amplitude. Under a proposed counting prescription motivated by Virasoro TQFT, we find agreement with the conjectured unit difference between the numbers of contributing manifolds associated to the two interaction terms in the potential. By contrast, counting all inequivalent surface embeddings separately would instead give a mismatch. This comparison highlights the importance of specifying the set of bulk topologies to be included in the gravitational path integral.