Papers

An illuminating probe of the dynamics of a line defect is the global geometry of its worldline. For a conformal line defect in a conformal field theory, sharp corners in the worldline, i.e. cusps, host dynamical degrees of freedom characterized in part by a spectrum of scaling dimensions, called cusp anomalous dimensions. We present various general bounds on cusp anomalous dimensions following from unitarity and cutting-and-gluing consistency of different defect geometries. We first establish, for cusps involving conjugate defects, that level crossings upon varying the cusp angle are forbidden between the lightest singlet cusp and any non-singlet cusp, proving that singlet cusps are the lightest. Then, we study line defects arranged in a rectangular geometry, which are subject to bootstrap constraints reminiscent of the spinless modular bootstrap. We find an analytic “magic" functional that produces an optimal and universal lower bound on the dimension of a right angle bare cusp in terms of the universal defect Casimir energy between the corresponding defect and its conjugate in flat space.

We analyze general properties of cusped defect lines embedded in generic conformal field theories (CFTs). We prove that suitably defined cusp scaling operators transform like primary operators under general conformal transformations. We show that, via the cusp operator expansion (COE), defects of general shape can be expanded in a basis of cusped defects. These findings are checked and exemplified in the case of the localized magnetic field defect. Finally, we derive analytic constraints on dynamical cusp data by making use of a crossing equation, and discuss possible numerical bootstrap applications of our results.

The fixed-ray escort integral representation expresses $\alpha$–$z$ Rényi divergence as an average over ordinary relative entropy of a family of escort states. Working in the standard UV-regulated density-matrix description of QFT subregions, we use this representation to derive an escort-averaged entanglement first law, an escort-averaged representation of the $\alpha$–$z$ information kernel, and an escort-averaged Bekenstein-type bound for ball-shaped regions in conformal field theories. For the conjectural $\alpha$–$z$ quantum null energy condition (QNEC), we obtain a quasi-local form in which the null energy is evaluated in an escort-averaged state and is corrected by an escort-transport term encoding the failure of escort formation to commute with restriction to a null-deformed region. The $z=\alpha$ specialization gives a similar quasi-local form of the Rényi QNEC for sandwiched Rényi divergence. We explicitly compute the Rényi QNEC, including the explicit escort transport term, for coherent-state excitations in a free scalar field theory. For the same coherent family, we obtain a positive $\alpha$–$z$ null Hessian, verifying the conjectured diagonal $\alpha$–$z$ QNEC for this family.

In these notes we deal with several field theoretical topics in the framework of the Quantum Field Theory as developed by Kadyshevsky. The main motivation for studying the Kadyshevsky formalism is that in the kadyshevsky graphs, in contrast with the Feynman graphs, the particles remain on the mass shell. This facilitates the use of phenomenological form factors, e.g. Gaussian ones. In the first part we construct the second quantised quasi-particle formalism, which is employed to develop the functional integral formalism. In the latter we develop the path-integral, the Schwinger-Symanzik equations, generalised Wightman functions, and the Kadyshevsky reduction formulas. In the second part we cover the topics: (i) the relation between the Feynman and Kadyshevsky perturbation theory, and (ii) the Gross-Jackiw method in the Kadyshevsky formalism. The latter method is applied to the kadyshevsky formalism for interaction Lagrangians with derivatives, in particular for pion-nucleon interactions: (i) pseudo-vector $NN\pi$-, (ii) vector $NN\rho$-, and (iii) gauge-invariant $\Delta_{33}N\pi$ coupling.

We develop a continuum framework for comparing the Gribov–Zwanziger and center-vortex descriptions of confinement through the gauge-invariant twisted partition function of the electric $\mathbb{Z}_N^{[1]}$ 1-form symmetry. A background 2-form field $B$, equivalently an 't~Hooft twist on a torus, labels a global sector and is not itself a dynamical center vortex. For a minimal irreducible twist on $T^4$, we derive the complete adjoint momentum lattice of $SU(N)$. The twisted spectrum is exactly the scalar spectrum on an enlarged torus with periods $(L_1,L_2,NL_3,NL_4)$ with the ordinary-torus sublattice removed. This yields a finite Faddeev–Popov gap at the flat representative and reduces twisted-minus-untwisted spectral traces to ordinary torus traces. For the refined Gribov–Zwanziger (RGZ) kernel, Poisson resummation gives an exact finite-volume Bessel-function winding sum with a universal center-twist projector. We evaluate the Gaussian one-loop integral at fixed RGZ parameters up to the finite-dimensional global zero-mode/stabilizer normalization. The Zwanziger determinants cancel, while the gauge-fixing/ghost sector leaves a universal massless primed determinant on $T^4$; the untwisted sector also contains constant gluon modes. The only normalization not fixed by the local quadratic Hessian is the relative zero-mode/stabilizer measure of the reducible untwisted and irreducibly twisted flat connections. We also derive closed finite-volume sources for the RGZ stationary equations. The massive response is exponentially suppressed at large volume, whereas the massless factor depends on the global zero-mode normalization. Thus the Gaussian calculation does not by itself establish the strong center-vortex-condensation criterion for $Z[B]/Z[0]$, but it isolates the remaining global normalization problem and separates a global twist from an actual dynamical vortex.

In this paper, we do not try to solve the measurement problem, but rather to properly formulate it. One of the reasons why it still lacks a precise, agreed definition is that the problem may take very different aspects depending on the interpretation of quantum mechanics embraced. Inspired by the methodology of theory-independent results like Bell's theorem, we propose to identify the common root of the puzzle in an interpretation-independent way i.e. as a property of the empirical statistics only, before deriving its philosophical consequences. The key observation is that quantum matter can not be described by a Kolmogorovian probabilistic theory. Arguing that the Kolmogorov axioms of probability theory are the postulates of epistemic uncertainty leads us to reformulate the measurement problem as the impossibility to build an ontology independent of epistemology for quantum matter. Said differently, there exists no God's-eye view on quantum systems. Although it is meaningless to solve the measurement problem as defined in this way, insofar as it is a feature of the universe's statistics, such a formulation may on the other hand bring side benefits. In particular, we argue that it allows to: (i) shed a new light on the variety of interpretations; (ii) propose a fundamental reason why quantum mechanics and general relativity are so incompatible, not relying on purely mathematical or technical arguments; (iii) guide the quest for quantum gravity.

We construct a gauge-invariant BF representative of a conical defect in Jackiw–Teitelboim gravity, with its elliptic direction fixed by the reconstruction of the gravitational variables. In the gravitational sector, the BF observable reproduces the metric defect insertion and its distributional curvature source, and fixes the holonomy around the defect to an elliptic conjugacy class. For a single defect on the disk, the position integral combines with the residual \(\mathrm{PSL}(2,\mathbb R)\) quotient, leaving a fixed elliptic sector. The exact boundary quantization of this sector gives the elementary kernel and one-defect disk amplitude directly, without using a matrix model. The same local BF operator describes both sharp and blunt defects. Their difference appears only when several defect positions are integrated. BF source composition makes the fractional deficits additive. Requiring a fused source to remain in the gravitational cone sector gives the admissibility condition for defect collisions, while positivity of the hyperbolic area on each component gives the corresponding stability condition. These conditions coincide with those for Hassett weighted curves. Combining these BF results with the known Hassett compactification and conical Weil–Petersson geometry yields the fixed-order genus-zero contact terms and recovers the cluster expansion of deformed JT gravity. Thus sharp and blunt defects differ through the compactified geometry of their relative positions, rather than through the elementary BF operator.

While spontaneous breaking of a discrete symmetry in one-dimensional classical systems with short-range interactions is absent, it is expected that a line defect embedded in a bulk criticality exhibits a stable discrete symmetry spontaneous breaking. Here, we investigate the behavior of a pinning-field line defect immersed in a 3D bulk that remains tuned to the $O(N)$ Wilson-Fisher critical point. Employing the fuzzy sphere technique, we provide convincing evidence of the existence of stable defect conformal fixed points, and we demonstrate their renormalization group stability by showing no relevant operator and less effective degrees of freedom than that at bulk fixed point via $g$-function. Moreover, we investigate the defect domain wall operator for various $N$, and we identify that it becomes irrelevance for $N\gtrsim 3$ but it is relevant for $N<3$.These evidence indicate that a one-dimensional defect coupled to a critical bulk cannot support a stable symmetry spontaneously broken defect fixed point due to domain wall proliferation for $N<3$ Wilson-Fisher universality, while in the case of $N \gtrsim 3$ a symmetry broken defect is possible.

We investigate the projective and resurgent structure of a spin hydrodynamic attractor in Bjorken expansion. We show that the nonlinear spin solution family is determined by the projective classes of the two dimensional linear solution space, with the attractor and repellor corresponding to two distinguished projective directions and the linear modes ratio generating the full one-parameter transseries tower. Using the projective transseries structure, we show analytically that the data of repellor are encoded in the Borel-Stokes structure of the attractor expansion. These results provide an explicit analytic realization of resurgence relations that are often extracted through high order expansions and numerical Borel analysis, and yield a unified description of the attractor, the repellor, and their Borel-Stokes connection in minimal causal spin hydrodynamics.

The odd- and even-parity gravitational perturbations of a Schwarzschild black hole are governed by the distinct Regge-Wheeler and Zerilli potentials, yet their quasinormal-mode (QNM) spectra are identical in vacuum. Building on our previous study of the odd-parity Regge-Wheeler spectrum [M. Ould El Hadj and S. R. Dolan, arXiv:2608.16283], we investigate the corresponding even-parity Zerilli problem and compare the two sectors under the same perturbation of amplitude $\epsilon$ at radius $r_0$. Using the Chandrasekhar-Detweiler relation, we derive an exact relation between the normalized Wronskians and show that Schwarzschild QNM isospectrality is not preserved under an identical nonzero localized defect. We find that the even- and odd-parity repelling-point branches approach the same Schwarzschild QNM frequencies at large $r_0$, with their first parity-dependent separation appearing at order $1/\mathcal R^2$, where $\mathcal R=r_{0*}/M$ is the dimensionless tortoise-coordinate location of the defect. The corresponding exceptional points (EPs) form two shifted sequences with the same asymptotic spacing in the tortoise coordinate, while their relative displacement is fixed by the phase of the asymptotic Chandrasekhar-Detweiler factor. The critical perturbation amplitudes share the same exponential decay rate in the two sectors, whereas the ratio of their asymptotic prefactors is fixed by the modulus of the same factor. We further find that the even- and odd-parity EPs connect the same neighboring QNM overtones, with nearly identical arclengths for the corresponding spectral bridges. Finally, the exceptional degeneracy is parity selective: at identical values of $(r_0,\epsilon)$, a pair of QNMs may coalesce at an EP in one parity sector while remaining distinct in the other, leading to a corresponding difference in the local pole structure of the ringdown response.

We construct an evolving wormhole cosmological model from a Morris–Thorne metric with a separable, time-dependent shape function in a spatially flat Friedmann–Lemaitre–Robertson–Walker background, deriving the corrected wormhole energy-momentum tensor and a volume-averaging procedure that yields a modified Friedmann equation with a redshift-dependent wormhole correction term. We show that the shape-function index and throat-evolution exponent combine into a single macroscopic exponent $\beta$, and we demonstrate that the resulting wormhole equation of state is consistent with this geometric averaging. All traversability conditions are verified. Confronting the model with cosmic chronometer, DESI Data Release~2 BAO, and standard BAO data across seven dataset combinations, our findings show that all combinations are mutually consistent, with the joint fit giving a present-day expansion rate intermediate between local and CMB-inferred values, a deceleration-to-acceleration transition consistent with independent determinations, and an effective dark-energy equation of state close to, but distinguishable from, a pure cosmological constant. The evolving throat radius offers a novel, geometry-specific observable for discriminating wormhole spacetimes from phenomenological dark-energy parametrisations.

We formalize the gauge structure of the Navier–Stokes equation for incompressible fluids, interpreting $\nabla\cdot\mathbf{v}=0$ as a gauge fixing analogous to the Coulomb gauge in electromagnetism. We construct the Martin–Siggia–Rose action and its full BRST symmetry, introducing BRST doublets for the Gribov parameter $\gamma$ and the monodromy phase $\theta$. Through a Higgs mechanism, $\gamma$ acquires a vacuum expectation value $\gamma_{0}$, generating a mass scale for the vorticity and the ghosts; we compute the one-loop effective potential and analyze vacuum stability. Intermittency — measured by the exponents $\zeta_{n}$ — is described by fluctuations of the Higgs field $\sigma$ around the condensate, via a Gribov-inspired log-Poisson hierarchy that satisfies exactly $\zeta_{3}=1$ (Kolmogorov's four-fifths law). Fits to DNS data favor filamentary vorticity structures, with $D_{f}\approx1$ (one parameter) or $D_{f}\approx2.1$, $\Delta\approx0.44$ (two parameters). The one-loop anomalous dimension in $d=3$, $\Delta_{\sigma}\approx0.50$, supports the identification $D_{f}=2\Delta_{\sigma}$. The formalism unifies classical hydrodynamics with gauge theory and spontaneous symmetry breaking, opening the study of turbulence and intermittency to quantum field theory methods.

Motivated by the conjectural existence of M-theory, we investigate a web of correspondences between enumerative invariants of a Calabi-Yau fivefold $Z$ with a torus action. This includes a correspondence between the fivefold Gromov-Witten invariants and K-theoretic Pandharipande-Thomas invariants of a threefold $X \subset Z$, mediated by so-called membrane indices, which generalise Gopakumar-Vafa invariants. We establish the correspondence for strip geometries for restricted torus actions and test it numerically for general torus actions. Further numerical evidence is provided for the closed vertex, local surfaces and local projective spaces. For the latter we present conjectural formulae for their low-degree membrane indices. When the fivefold is the product of the affine plane with a suitable toric variety, we prove geometric engineering and equate the generating series of Pandharipande-Thomas invariants with the corresponding instanton partition function while equality with the Gromov-Witten series is probed numerically.

In precision holography, the Euclidean on-shell action of type IIB supergravity often fails to reproduce the leading large-$N$ free energy of the dual field theory: the type IIB pseudo action, for instance, vanishes identically on the $\mathrm{EAdS}_5\times S^5$ background. We address this issue by revisiting the boundary-value problem of the Euclidean type IIB pseudo action from first principles. Classifying the admissible boundary conditions through the variational principle, we construct a generalized pseudo action whose boundary terms implement the choice of ensemble — fixed potentials versus fixed quantized Page charges — in which the holographic comparison is performed. For the fixed five-form-charge ensemble, the resulting boundary term reproduces the recently proposed topological correction to the Pasti–Sorokin–Tonin formulation of type IIB supergravity for holographic backgrounds of interest. We then test the generalized pseudo action on two complementary backgrounds: the $\mathrm{EAdS}_3\times S^3\times M_4$ near-horizon geometry of the D1-D5 system and the warped $\mathrm{EAdS}_6\times S^2\times\Sigma$ solutions dual to five-dimensional SCFTs. In both cases the ten-dimensional on-shell action agrees exactly with that of the corresponding lower-dimensional supergravity, and thereby with the leading large-$N$ free energy of the dual SCFT. Our results establish the choice of boundary conditions — and hence of ensemble — as an essential ingredient of precision holography directly in type IIB supergravity, extending recent analyses in eleven-dimensional supergravity.

We show that Gravity from Entropy (GfE) exhibits a tensor-propagation pathology on generic FLRW backgrounds. In vacuum, in the symmetry-inheriting single-multiplet sector, and for the algebraic perfect-fluid constitutive embedding, the strict-principal TT system has a nonzero real characteristic only when \(\dot H=K/a^2\). Away from this locus the temporal principal roots become complex, signaling a high-frequency hyperbolicity obstruction. Under the stated isotropy assumptions, a rank theorem further shows that one foundational multiplet cannot provide the isotropic bivector response needed to remove this problem.

The strong gravitational interaction of counter-propagating quantum field modes is of foundational importance to the trans-Planckian problem of black hole horizons. This article, in memory of Renaud Parentani, is primarily an exposition of Renaud's attempt, using perturbation theory, a large $N$ approximation, and spherical reduction, to capture a mechanism by which those interactions might quench the trans-Planckian near-horizon quantum field correlations. Before giving a detailed account of Renaud's calculation, the trans-Planckian problem is briefly introduced, and the paper concludes with a discussion of related issues and questions.

Unlike standard quantum teleportation, many-body teleportation uses scrambling to transmit quantum information. In this protocol, initially localized information spreads over many degrees of freedom and is later refocused at the receiver by a simple coupling between the systems, followed by further many-body evolution. The protocol was developed from models of traversable wormholes in holography and has become a useful probe of scrambling. In particular, it can distinguish genuine scrambling from decoherence or noise when out-of-time-order correlators fail, and can reveal signatures of different scrambling mechanisms, including the distinctive behavior expected in holographic systems. Holography predicts that related protocols can transmit information between selected boundaries of multi-boundary wormhole geometries. Motivated by this setting, we study single-qubit many-body teleportation among three systems of qubits. The initial state consists of EPR pairs distributed among them, providing a simple analogue of an infinite-temperature three-boundary holographic state. We analyze the protocol with one-dimensional and all-to-all dynamics, both analytically and numerically using random circuits. We find that the third system suppresses teleportation once the spreading message reaches the region of qubits that are entangled with it. In one dimension, both the minimum coupling required for successful teleportation and the fidelity depend on the distance from the injection site to this region, a feature reminiscent of holographic causal shadows. For all-to-all dynamics, successful teleportation is instead restricted to early times and to sufficiently few qubits entangled with the third system. A third system therefore provides spatial, or subsystem, resolution of information spreading that is absent from the two-sided protocol. Our results offer a step toward many-body teleportation networks.

The structure of non-invertible symmetries in 2D CFT is closely tied to the algebra of preserved holomorphic fields, its representation theory, and its embedding in the full chiral algebra of the CFT. Unfortunately, finding new embeddings of a chiral algebra into another is a difficult mathematical problem, and one of the major obstacles in the pursue of new and exotic categories of non-invertible symmetries. In this work, we describe a simple general technique that leads to a number of new non-trivial results in this direction: (1) For the holomorphic Monster CFT $V^\natural$, we show that for every `Fricke' non-anomalous Monster element of order $N$, there is an embedding of the parafermion algebra $\frac{su(2)_N}{u(1)}$ in $V^\natural$, we compute the characters of its commutant, and describe the topological defects preserving these subalgebras. (2) We provide an easy-to-check sufficient condition for a holomorphic VOA $V$ to be self-orbifold under a cyclic group of (invertible) symmetries, and determine the associated duality defect. (3) We find several new topological defects in CFTs arising from heterotic strings on $T^4$. (4) We prove a number of VOA embeddings and topological defects in the Leech lattice CFT, in Schellekens theories, and other CFTs of various central charges, and suggest several generalizations of our methods.

It was recently shown by Yeliussizov \cite{Yeliussizov} that integer partitions in dimensions $d \geq 7$ asymptotically grow strictly faster than MacMahon numbers. As MacMahon numbers match with integer partitions in dimensions $d = 1,2$, the comparison of asymptotics of integer partitions with MacMahon numbers in intermediate dimensions ($d = 3,4,5,6$) is an open question. In this work, we perform Markov chain Monte Carlo (MCMC) simulations till $N=15000$ by using adaptive weight learning followed by conventional MCMC steps to numerically estimate the asymptotics of integer partitions in these intermediate dimensions. We numerically establish that in these intermediate dimensions, partitions asymptotically grow faster than MacMahon numbers. More specifically, assuming that the limits exist, we show: $\lim_{n\to\infty}n^{-3/4}\log p_3(n) = 1.8196 \pm 0.0019$, $\lim_{n\to\infty}n^{-4/5}\log p_4(n) = 1.7215 \pm 0.0045$, $\lim_{n\to\infty}n^{-5/6}\log p_5(n) = 1.6521 \pm 0.0059$, and $\lim_{n\to\infty}\log n^{-6/7}p_6(n) = 1.652 \pm 0.021$ for partitions in dimensions $d=3,4,5,$ and $6$ respectively. These numbers are all larger than MacMahon leading order asymptotic coefficients of $1.7898, 1.6614, 1.5737,$ and $1.509$ respectively. Additionally, we also find estimates for some of the sub-leading asymptotic terms in $\log p_d(n)$ in each of the dimensions.

We study general holographic fluctuation equations with apparent singularities, and the associated spectral functions. We consider the regime where an apparent singularity approaches the boundary, for which the near-boundary behavior of solutions can be determined via an inner/outer matching type of calculation. Depending on properties of the equation, we find that the merging of an apparent singularity with the boundary may generate either a zero or a pole for the corresponding spectral function. Our results also indicate that the recently introduced holographic product formula still applies in the presence of apparent singularities.

The free energy of any CFT, $ \ln Z(\beta; \omega_i)$, admits two expansions: high temperature ($\beta \rightarrow 0$) and fast rotation ($\omega_i \rightarrow 1$). We demonstrate that in $4d$, locality of the thermal effective action forces $\ln Z$ to take a simple analytic form at all orders in the high temperature expansion, and further imposes an infinite number of sharp relations on the coefficients in this expansion. All are homogeneous, except at order $\beta^1$ due to the Weyl anomaly. From this, the $a$-anomaly can be extracted from the partition function. The relations resum in the fast-spinning expansion into differential equations in $\beta$ obeyed by the semi-universal limit and its corrections. We verify the relations in a variety of CFTs. We generalize to any even $d$, but find no similar relations at odd $d$.

The phase coherence of primordial perturbations shapes the acoustic peaks of the CMB and is regarded as a key signature of inflation. Inflationary scenarios at different energy scales, thus with different durations, are commonly expected to leave different levels of coherence. We show this expectation fails: because the curvature perturbation is conserved on super-Hubble scales, the coherence at recombination inherits a value fixed by the observed primordial spectrum alone. This holds irrespective of the inflationary energy scale and the subsequent expansion history.

We develop a canonical ADM framework for gravitational backreaction during inflation. Our approach extends the formalism used to compute cosmological correlators by applying it to the evolution of the quantum background, which we identify with the metric one-point function. The aim is to assess the quantum stability of inflationary geometries under gravitational backreaction. Within this framework, the backreaction is determined by the expectation values of the Hamiltonian constraint and the equations of motion for the spatial metric. Working in the exact de Sitter limit, we apply the framework to a massless minimally coupled spectator scalar field and the physical graviton polarizations. At one loop, their backreaction renormalizes the relation between the cosmological constant and the Hubble parameter without inducing any secular departure from de Sitter evolution, in agreement with previous results. We perform the calculation using a hard momentum cutoff and show that a fixed physical cutoff allows the homogeneous background equations to be renormalized with time- and background-independent coefficients, in contrast to a fixed comoving cutoff. Finally, we demonstrate that the explicit representation of the backreaction depends on the gauge condition imposed on the metric fluctuations, as well as on the background-fluctuation split. Nevertheless, these different representations are related by a gauge transformation and are therefore physically equivalent.

Extreme-mass-ratio inspirals (EMRIs) provide a unique laboratory for probing strong-field gravity and complex relativistic dynamics. We study a tidally deformed EMRI composed of a stellar-mass secondary orbiting a supermassive (non-)rotating black hole embedded in an external, adiabatically varying tidal environment. These systems provide a restricted, yet astrophysically motivated, realization of the relativistic three-body problem, expected to appear in active galactic nuclei, with a clear hierarchy of masses and radiation-reaction timescales. The external tidal deformation breaks the axisymmetry of the Kerr spacetime, rendering the geodesic dynamics non-integrable and giving rise to chaotic motion. The resulting signature of non-integrability is characterized through Poincaré maps and rotation curves constructed from the ratios of the fundamental frequencies of bound radial, polar, and azimuthal motion. We identify two prominent plateaus whose widths increase with the tidal field amplitude, signaling a transition from weak to strong chaos. We then demonstrate the sensitivity of the chaotic dynamics to the orientation of the orbit relative to the tidal field. We further analyze the proper-time evolution of the action-angle variables, showing that the angle combinations associated with the dominant commensurabilities are phase locked, thereby allowing the associated tidal contributions to induce secular changes in the constants of motion, whereas off-plateau angle combinations circulate. These results clarify the dynamical significance of the prominent plateaus and provide a novel phase-space characterization of tidal resonances in EMRIs. Finally, we discuss the potential role of radiation-reaction effects in driving EMRIs through tidal island crossings and the implications for gravitational-wave inference with future detectors.

In infinite-distance limits of scalar field moduli spaces in quantum gravity, particle masses, brane tensions, and scalar field potentials scale exponentially with geodesic distance. Previous work has shown that the exponential decay rates of particle masses and brane tensions admit a discrete classification. In this work, we extend this classification to the case of scalar field potentials. We find that leading contributions to the potential typically scale with tensions of codimension-1 branes as $V \sim T_{d-1}^2$ or codimension-0 branes as $V \sim T_d$, and these relations hold formally even when the associated branes are absent from the spectrum. As a result, the taxonomy rules for potentials are intimately connected to the brane taxonomy rules. More generally, potential contributions can be labeled by a collection of integers, which correspond physically to their transformation properties under Weyl rescalings and their order in the string loop expansion. This implies that the vector $\vec v = - \vec \nabla \log V$ is lattice-valued, and indeed it lies in precisely the same lattice as the analogous vectors $\vec \alpha = - \vec \nabla \log T_d$ for codimension-0 branes of tension $T_d$. We verify our taxonomy rules in various examples in string theory. We show that these rules imply that sums of positive potential terms satisfy the Strong Asymptotic de Sitter Conjecture, which requires $|\vec \nabla \log V| \geq 2/\sqrt{d-2}$ in asymptotic regimes of scalar field moduli space, and they imply that higher-derivative gravitational corrections are suppressed by powers of the species scale.

The late-time ringdown dynamics of near-extremal black holes (BHs) are expected to be dominated by zero-damped modes (ZDMs), whose decay rates are parametrically suppressed relative to those of ordinary quasinormal modes. In this paper, we demonstrate that exact WKB methods provide an exceptionally powerful framework for analyzing the ZDM spectrum of near-extremal Reissner–Nordström (RN) BHs. Focusing on massless, neutral scalar modes propagating on an RN background, we present the full Stokes geometry derived from the radial eigenvalue problem and establish the corresponding exact quantization condition (EQC). Our analytic computation of the Voros symbols entering the EQC achieves higher-order accuracy for the ZDM spectrum compared to previous studies and is systematically improvable. Ergo, this work serves as a proof of concept for investigations of ZDM spectra of other systems using exact WKB methods.

Motivated by the question of whether the internal scales of a compactification can be parametrically decoupled from the external curvature scale, and by the possibility of probing such vacua holographically, we construct the first AdS$_2$ flux vacua with parametric scale separation. We compactify type II string theory on a $G_2$ structure orbifold times a circle in the presence of smeared spacetime-filling O1/O5-planes or O4/O8-planes, together with NSNS and RR fluxes. We derive the two-dimensional dilaton-gravity effective theory and exhibit families of vacua in which unbounded $F_5$ and $H_7$ fluxes provide parametric control in type IIB, while unbounded $F_4$, $F_8$, and $H_7$ fluxes provide parametric control in type IIA. For large flux quanta, the string coupling becomes parametrically weak, all internal bulk radii become parametrically large in string units, and the Kaluza–Klein scale separates from the $\mathrm{AdS}_2$ curvature scale. We analyze the ten-dimensional Killing-spinor equations and identify parametric branches preserving $\mathcal N=(1,1)$ supersymmetry in two dimensions. We explain how our geometrically scale-separated AdS$_2$ vacua are compatible with a recent no-go theorem for scale separation in theories with extended supersymmetry. Finally, we discuss various T-dualities leading to other type IIB and type IIA compactifications on $G_2$ structure spaces times a circle and $SU(3)$ structure spaces times a two-torus.

Using the newly developed $3$d quantum trace map, we compile more evidence for the length conjecture, a refinement of the all-order volume conjecture that incorporates insertions of additional links in the skein module of the knot complement. In particular, we prove that the length conjecture holds up to first order for an infinite family of twist knots. Along the way, we form a conjecture that the $3$d quantum trace map behaves naturally with respect to Dehn filling.

The equivalence classes of boundary conditions of a gauge theory on a two-dimensional orbifold are the fibres of a marginal map, indexed by an affine semigroup: one generator per alphabet label, graded by weight, embedded by its local data at the fixed points. This note identifies that semigroup. Without weights the configuration has a name and a literature, whose results about our cases are attributed here: over $\mathbb{Z}_2$ it is the cut configuration of an explicit graph in the sense of Sturmfels-Sullivant — the four-cycle for $T^2/\mathbb{Z}_2$, the wheel $W_4$ for $S^1/\mathbb{Z}_2\times S^1/\mathbb{Z}_2$ — verified as an equality of configurations; over $\mathbb{Z}_m$ with equal cone orders, the group-based phylogenetic model on a claw tree; with unequal orders, a mixed-order variant we do not find in the literature; for higher products, the binary hierarchical model of a cross-polytope boundary complex. The product orbifold's ring is a row of a 2008 table — codimension, degree, minimal generators, normality — every invariant of which our machinery reproduced without knowing of it. What none of the three covers is the alphabet with weights, which arise from induction to higher-dimensional irreducibles of a non-abelian space group and from conjugate-pair recombination over real or quaternionic ground. That sector is adjacent to, but not identified with, the non-abelian direction Sturmfels and Sullivant raised in 2005, and is where our contributions sit: gluing trees for the weighted alphabets and the orthogonal and symplectic columns, and the group-based model on the tripod, a complete intersection exactly when the finite abelian group has order at most three. The first group beyond $\mathbb{Z}_3$ separates local from global: the $\mathbb{Z}_4$ tripod is a complete intersection on the Zariski-open set the phylogenetics literature works in, and not globally.

To overcome the failure of the conventional non-relativistic description of statistics in strong gravitational fields, we develop a covariant theory for a photon gas in curved spacetime, starting from the Boltzmann equation and employing the relaxation time approximation. The transport coefficients are computed up to second order, which are not a massless limit of the massive-particle results due to the fundamentally different phase-space geometry of null particles. At second order, the gravitational field renders the coefficients tensor-valued and induces transverse fluxes, analogous to the Hall effect. Using the first-order results, we derive relativistic generalizations of Fick's and Fourier's laws and obtain the radiation diffusion equation for spherically symmetric accretion disks. This provides a covariant description of radiative transport in strong gravitational fields for high-energy astrophysical applications.