Papers

We study deformation of supersymmetric $t$-confining (truly confininig) gauge theories with small anomaly mediation of supersymmetry breaking. We identify breaking pattern of global symmetries in the theories. These results can be compared in priciple to lattice simulation of non-supersymmetric theories (except for one of the cases where the theory is pseudoreal and chiral).

We propose a novel analytic approach to the study of multi-component FLRW cosmologies and their perturbations. The dynamics is triggered by a single scalar field with a scalar potential codifying the energy density and pressure of the multi-component fluid. This description unifies standard Big Bang cosmologies, models of inflation and dark energy under a unique framework. The key to integrability is to express the scalar potential in terms of the Hubble function $H(\phi)$ that plays the role of a fake superpotential, turning the dynamics into a first order problem, that may be analytically solved in a suitable time coordinate. In this framework, we propose integrable inflationary models with similar properties to the ones analysed in the literature and compatible with observations. Finally, we study scalar and tensor cosmological perturbations in each model by integrating Mukhanov-Sasaki equations via numerical and (semi-)analytic techniques. This allow us to compute the power spectrum, the spectral indices and the tensor-to-scalar ratio beyond the slow-roll approximation and compare our general results {against} the currently available observations and the theoretical predictions based on the slow-roll approximation.

We develop an ODE/IM-based formulation for the thermal partition function and the spectral zeta function of the homogeneous Hermitian and PT-symmetric oscillators. For both classes of systems, the quantization condition can be expressed using the counting function $a(E)$, which can be solved via the Destri-de Vega equation of the integrable model. We then express the partition function and spectral zeta function as contour integrals involving the counting function, thereby providing a direct bridge between quantum spectral functions and integrable models.

We study static, spherically symmetric axion–dilaton solutions of the tree-level four-dimensional string effective action. Using the sigma-model structure of the scalar sector, we show that the full family of static, spherically symmetric and asymptotically flat solutions is obtained as the $SL(2,\mathbb R)$ orbit of the pure-dilaton FJNW solution, and we characterize the associated axion–dilaton charge space. We then analyze the perturbative regime of these solutions by comparing the onset of $\alpha'$ curvature corrections with that of string-loop corrections. Finally, we apply the string–black-hole correspondence criterion to the FJNW family by evaluating the local $\alpha'$ curvature diagnostic at the physical size $R_{\rm typ}$ of a highly excited string state. With the normalization fixed on the Schwarzschild branch, Schwarzschild saturates the nominal $\alpha'$ threshold at the correspondence surface, whereas every scalar-haired FJNW branch lies above it. More generally, independently of the common overall normalization within the matching prescription, every nonzero-hair branch has a larger curvature diagnostic at the correspondence surface than Schwarzschild. Away from the correspondence point, scalar-haired exteriors may remain under $\alpha'$ control at sufficiently weak local self-gravity and may provide perturbatively controlled long-distance fields of highly excited string states whenever the local string coupling also remains weak.

We study the entanglement Hamiltonian of an infinite hopping chain in its ground state, after partial projective measurements in the occupation basis. For a segment separated by two measurement regions from the rest of the chain, we show that the reduced density matrix can be related to a grand-canonical state via a conformal mapping and a gauge transformation in the underlying field-theory description. The entanglement Hamiltonian is then described by a local inverse temperature that vanishes as a square root around the endpoints and is independent of the particular measurement outcome. In sharp contrast, the local chemical potential is shown to be related to the induced charge density in the segment. Hence the entanglement Hamiltonian of a post-selected state contains much more information on the measurement outcome than the respective entropy.

We introduce a second-order mean-field description of the four-dimensional Euclidean $\phi^4$ model within the Wilson–Polchinski renormalization-group framework. The construction is based on the connected amputated Schwinger functions evaluated at the symmetric momentum configurations $ (p,-p,\ldots,p,-p)$, which are decomposed into a momentum-independent component, a component quadratic in $p$, and a higher-order remainder. The first two components are chosen to satisfy a closed nonlinear hierarchy. We prove the existence of solutions to this hierarchy for arbitrary positive bare coupling and establish their convergence to the Gaussian fixed point as the ultraviolet cutoff is removed. In particular, both the momentum-independent and the quadratic momentum sectors are asymptotically trivial.

We construct the complete full-color three-loop five-point integrand of N=4 super-Yang–Mills theory in a representation that manifestly satisfies color–kinematics duality. Its double copy gives the corresponding N=8 supergravity integrand. For four-dimensional external states, we evaluate the ultraviolet poles of both amplitudes in the critical dimension, Dc=6. Extending the external-state dependence to D dimensions is subtle. We consider a candidate replacement of the four-dimensional prefactors by expressions built from D-dimensional tree amplitudes. It reproduces the open-string prediction for the SYM pole with generic D-dimensional external states, whereas the corresponding gravity expression differs from the string-inspired one by an evanescent term.

We study the gravitational effective action induced, at first order in the deformation parameter, by non-local $T\bar T$-like deformations of quantum field theories. Using a heat-kernel formulation, we extract the local geometric terms generated by stress-tensor two-point functions, and apply the construction to free fermions, massive Maxwell theory, and second-order Yang-Mills theory. While the resulting coefficients are generally model dependent, conformal field theories contain a universal sector fixed by the central charge $C_T$. After regularization and renormalization, this sector yields finite, scheme-independent contributions organized into a finite set of curvature invariants. We further analyze trace-trace deformations, for which the relevant contact terms are determined by the Weyl anomaly, and derive the corresponding finite gravitational action for a general class of minimal non-local kernels. These results provide a quantum effective-action realization of induced gravity in which universal conformal data determine calculable contributions to the emergent geometric response.

We study black hole formation resulting from the collapse of a homogeneous and isotropic dust ball within a framework built upon loop quantum cosmology. Using loop dynamics formulated for Lemaitre-Tolman-Bondi spacetimes—which reduce to the asymmetric loop quantum cosmological bounce scenario—we analyze the dust ball undergoing power-law contraction followed by a de Sitter-like expansion. We discover an emergence of a physical shock at the dust ball surface, characterized by a continuous induced metric and a discontinuous extrinsic curvature arising from a dynamical mismatch between the expanding interior and the contracting exterior vacuum shells. Furthermore, we explicitly derive two variants of Schwarzschild-like line elements for the vacuum sector, and we demonstrate that the resulting spacetime is geodesically complete featuring a rich causal structure. This establishes, for the first time, fully dynamical regular black hole formation within a framework consistent with loop quantum cosmology.

We investigate gravitational and Kerr-Newman extensions of an information-theoretic black-hole entropy that satisfies the Nernst formulation of the third law of thermodynamics. The entropy is identified with the Kullback-Leibler divergence between a mass-dependent Bernoulli ensemble and an unbiased reference ensemble, and therefore measures relative information rather than the logarithm of the number of black-hole microstates. We show perturbatively that its temperature and entropy can be reproduced by an infrared deformation of General Relativity. To linear order in the deformation couplings, the surface-gravity temperature and the Wald entropy agree with the information-theoretic results. In an explicit realization, the matching generates a positive effective cosmological term whose smallness is related to the large microscopic parameter $N$. We also propose an extension to Kerr-Newman black holes based on the irreducible mass. This construction preserves the connection with the horizon area and the semiclassical limit, while distinguishing geometrical extremality from the universal statistical-freezing endpoint, which is independent of angular momentum and charge.

Although the Bekenstein-Hawking area law is consistent with the first and second laws of black hole thermodynamics, it appears to be in conflict with the third law, which in the Nernst formulation states that the entropy should either vanish or approach a universal constant in the zero-temperature limit. We argue that this tension reflects a limitation of the semiclassical area law rather than a fundamental feature of black hole thermodynamics. On this basis, we obtain an entropy formula that is consistent with the third law, and approaches Bekenstein-Hawking entropy in the high-temperature limit. The resulting entropy admits a simple microscopic interpretation, and it can be written as the Kullback-Leibler divergence between a mass-biased Bernoulli distribution and the uniform distribution on N microscopic bits. From this perspective, the thermodynamic black hole entropy admits an information-theoretic representation as an entropy deficit, namely as the relative entropy between the black hole ensemble and a maximally mixed reference ensemble. The Bekenstein-Hawking area law then emerges as the leading term in an $1/N$ expansion, while a universal mass scale $M_0=\sqrt{N}\,M_P$, interpreted as an absolute upper bound on the black hole mass, controls the bias of the underlying microscopic ensemble. The subleading terms represent finite-information corrections to the classical area law.

We uncover a double-copy relation between chiral and conformal anomalies in four-dimensional conformal field theory. We show that this relation extends from local anomaly structures to complete momentum-space three-point correlators and, through their flat-space limits, to five-dimensional scattering amplitudes. In particular, the parity-odd current correlators associated with the chiral anomaly reduce, in the flat-space limit, to a universal amplitude generated by a Chern–Simons interaction. Squaring these anomalous current correlators reproduces the contribution to the stress-tensor three-point function $\langle TTT\rangle$, controlled by the conformal anomaly, thereby establishing a direct link between chiral- and conformal-anomaly structures.

An axion driven toward a thermal minimum need not remain a coherent condensate. We derive the coupled attenuation of the field mean and production of stochastic momentum modes in an expanding plasma. A single momentum dependent optical depth partitions every mode between coherent power and Bose occupation, placing standard misalignment, partial relaxation, and stochastic production in one dynamical relation. Finite spatial and temporal response suppresses high momentum production, so the stochastic relic has lower mean momentum and a shorter free streaming length than an equilibrium population at fixed mass and bath temperature. A weakly coupled realization produces the dark matter abundance, reduces inherited coherent isocurvature, and confines production correlations to scales removed by collisionless propagation. Thermal relaxation therefore determines the composition, momentum distribution, and transported structure of axion dark matter.

We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss quantifies Bob's inability to retrodict with certainty which state Alice sent through the channel. By minimizing this measure over all possible pure state ensemble decompositions of a fixed state $\rho$, and over all POVMs on the output of a channel $\mathcal{E}$, we arrive at an intrinsic notion of information loss for any state-channel pair $(\rho,\mathcal{E})$. We show that the vanishing of information loss with respect to all states supported on a fixed codespace $\mathcal{H}_{\text{code}}$ is equivalent to a condition we term universal pristineness, which ensures that orthogonal pure states in $\mathcal{H}_{\text{code}}$ get sent via the channel $\mathcal{E}$ to possibly mixed states whose supports are orthogonal. Moreover, we prove universal pristineness is equivalent to the Knill-Laflamme conditions in quantum error correction, which are necessary and sufficient for the existence of a perfect recovery channel for all states supported on $\mathcal{H}_{\text{code}}$. As an application, we apply our framework to the Hayden-Preskill model of black hole evaporation, demonstrating that the evaporation channel becomes asymptotically universally pristine, thereby providing a purely channel-theoretic formulation of Page-time information retrieval.

We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger–Horne–Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice–Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter—the sharp distinction from the fermionic case, where it stays bounded—while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.

Starting from SU(N) on the lattice, we give a rigorous derivation of the Dyson–Schwinger equations in the continuum limit. We formulate the Dyson–Schwinger identities for the lattice Yang–Mills theory directly in terms of the link variables $U_\mu(m)\in SU(N)$, exploiting the invariance of the Haar measure under left group translations. This provides an exact lattice derivation of the corresponding master equation for the Wilson action, expressed through left-invariant Lie derivatives acting on individual links. Because the construction is carried out directly on the compact gauge group, it avoids the ambiguities associated with introducing Lie-algebra valued gauge potentials as primary integration variables at finite lattice spacing. For practical applications, in a second part we then break down the gauge degree of freedom by choosing Feynman gauge. We analyze the continuum-limit form of the resulting lattice identities and derive equations for the one- and two-point connected functions. Under a further simplifying reduction, these equations close to a tractable scalar system. Our results establish a direct bridge between exact lattice identities and the functional equations commonly used in continuum nonperturbative studies of Yang–Mills theory.

We present a unified derivation of the Galilean and Carrollian limits of the massive Dirac action based on a similarity transformation depending on the mass and the speed of light. The two choices of Dirac conjugation, combined with different mass scalings, generate distinct families of limiting actions. This construction recovers known Galilei and Carroll fermion models and yields new systems, one in each regime. We classify a sufficient set of boost-compatible local (self-)interactions, which includes Nambu–Jona-Lasinio (NJL). The new Galilean free action possesses a local fermionic gauge symmetry that eliminates its local field content. A selected quartic interaction, preserving the Bargmann boost, explicitly breaks the original fermionic gauge symmetry so that the argument that eliminates the field content no longer applies. The NJL limit interaction merely deforms the realization of that gauge symmetry. We show that the energy parameter in several Carroll actions can be eliminated by a time-dependent phase redefinition; conversely, in the new Carrollian extension the energy cannot be removed.

We propose a systematic optimization framework for determining the sum rule window in QCD Laplace sum rules. Instead of relying primarily on fixed convergence percentages and visual plateau selection, the procedure combines an OPE entropy criterion, local mass stationarity, and a correlated analysis of the Laplace parameter $\tau$, the continuum threshold $t_c$, and the interpolating-current mixing angle $\theta$. The normalized OPE entropy is introduced to quantify the redistribution of the QCD contributions between the perturbative and nonperturbative sectors and to delimit an initial Working Region. This domain is subsequently refined by minimizing the residual variation of the mass estimator and requiring weak sensitivity to the continuum threshold and to the current composition. As an application, we study the lowest fully charmed tetraquark state with quantum numbers $J^{PC}=2^{++}$ using a mixed diquark–antidiquark and meson–meson interpolating current. The optimization selects $\theta=17.2^\circ\pm0.4^\circ$, $\sqrt{t_c}=7.08\pm0.08~\mathrm{GeV}$, and $\tau=0.410\pm0.010~\mathrm{GeV}^{-2}$, leading to the mass prediction $M_{c\bar c c\bar c}^{2^{++}}=(6.32\pm0.11)~\mathrm{GeV}$. The predicted state lies in the near-threshold region of the di-$J/\psi$ spectrum and is compatible, within uncertainties, with the lowest resonant component reported by ATLAS and with the enhancement parametrized as $BW_0$ in the recent CMS publication. The proposed framework provides a reproducible way of identifying finite domains of reduced auxiliary-parameter sensitivity and of incorporating the remaining dependence into the final uncertainty.

Beyond conventional Higgs-family and general CP transformations, one may also consider a broader class of non-standard "GOOFy" transformations, in which the scalar fields and their conjugates are assigned related but inequivalent transformations. Although these transformations are not symmetries of a full Lagrangian in the conventional sense, some nevertheless stabilise the scalar potential. Their impact on the quadratic sector has not yet been systematically classified. We develop a sign-orbit technique to determine the bilinear structures compatible with these transformations. Applied to three-Higgs-doublet models, and formulated so as to extend to larger multi-Higgs sectors, the method shows that a non-vanishing GOOFy-compatible quadratic sector exists only when two independent conditions are met: the underlying group admits a non-trivial sign character, and that character is realised within the tensor product of the scalar representation and its conjugate. As a key consequence, we demonstrate that the renormalisation-group stability of the $r_0 \to -r_0$ manifold in isolation is not a generic feature of multi-Higgs potentials, but rather a direct consequence of special algebraic properties of $SU(2)$. These results provide a classification of the admissible GOOFy quadratic structures and their invariant bilinear subspaces, highlighting the algebraic obstructions to their renormalisation-group stability.

3-forms are interesting fields to study in the cosmological context for numerous reasons, such as being candidates for explaining inflation and dark energy. The background evolution of a 3-form field is similar to but distinguishable from a scalar field in an expanding universe, and its tensorial structure allows for unique couplings that cannot be experienced by canonical scalars. In this work, we explore the possibility that 3-form dark energy can explain cosmic birefringence. We consider two EFT-inspired couplings between the 3-form and the photon, and compute the birefringence angle $\beta$. We find that a dimension-6 gauge-invariant operator necessitates an extremely large coupling to explain $\beta\sim0.3^\circ$, the value suggested by observations of recent cosmic microwave background radiation. Conversely, a dimension-4 operator can accommodate $\beta\sim0.3^\circ$ at the expense exciting the longitudinal mode of the photon. Interestingly, demanding a self-consistent decoupling limit implies the photon mass lies within a few orders of magnitude of $H_0$. We also derive `universal' profiles for $\beta(z)$, finding the $\beta$ from the dimension-4 operator is insensitive to the form of the 3-form potential but is sensitive to the initial conditions. Contrarily, the dimension-6 operator is highly sensitive to the form of the potential. We finally compare the universal profiles to that of axion-like particle (ALP) dark energy and an ultralight massive 3-form, the latter obtained from numerically integrated cosmological histories consistent with $\Lambda$CDM up to low redshift. Our results show that birefringence from 3-form dark energy can both mimic that from an ALP or be distinguishable, depending on the field configuration in the early universe.

Electric-magnetic self-duality of the $\mathbb{Z}_2$ gauge theory, realized microscopically as a half-lattice-translation exchanging electric charge and magnetic flux, has been an influential example of a duality symmetry with an exact lattice realization. We construct the first non-Abelian generalization of this construction: a lattice model of the $S_3$ quantum double $\mathcal{D}(S_3)$ on a tensor product Hilbert space in which the $\mathbb{Z}^{\mathrm{em}}_2$ anyon-permutation symmetry, exchanging the non-Abelian chargeon $C$ and fluxon $F$, is realized via lattice translation. Consequently we find that the zigzag boundary termination of the model realizes, without fine-tuning, a gapless critical edge state described by the tetracritical Ising CFT. The bulk admits three independent $\mathbb{Z}_2^{\mathrm{em}}$-preserving bosonic perturbations, driving $\mathcal{D}(S_3)$ into distinct gapped phases. We analyze these transitions by three independent methods: category-theoretic anyon condensation, microscopic lattice Hamiltonians, and Chern-Simons-Higgs theory, which all agree, yielding a unified picture. These examples motivate a minimal-condensation principle: proliferating a bosonic anyon generically drives condensation of a minimal condensable algebra containing it, with symmetry-related condensates appearing as degenerate vacua that spontaneously break the anyon-permutation symmetry. Our model construction extends to an infinite family of self-dual dihedral quantum doubles $\mathcal{D}(D_{2n})$. Notably, each model is sign-problem-free, opening the door to large-scale numerical exploration of the phases of non-Abelian Chern-Simons-Higgs theories.

We study the leading adiabatic response of magnetic GHS black holes in massless Einstein-Maxwell-dilaton theory to a prescribed exterior modulus varying slowly in advanced time. In ingoing Eddington-Finkelstein coordinates with the exact areal radius, we derive the time-dependent spherical equations and expand about a slowly evolving instantaneous static GHS representative, keeping its horizon distinct from the exact dynamical marginal horizon. The magnetic GHS family realizes the canonical-slice and Fredholm framework developed in the companion paper. Its integrability yields in closed form the canonical tangent, the finite-rank source profile, a horizon-regular solution of the auxiliary inhomogeneous equation, and a globally regular generator of the sliced-operator kernel. For the leading Robin functional arising in the massless large-radius overlap, we evaluate the Fredholm denominator analytically and prove that it is strictly positive on the charged non-extremal branch. This remains true where the conventional normalization of the kernel generator degenerates, showing that these loci are normalization singularities rather than degeneracies of the kernel mode. Within the controlled large-radius overlap regime, this positivity proves existence and uniqueness of the completed leading-order quasi-static near-zone problem. We then solve the forced radial equation explicitly. The scalar lag is the sum of a universal forced profile and a sliced homogeneous mode whose amplitude is fixed by the exterior matching datum. The mass lag follows algebraically from the radial constraint, and the lapse lag from a single elementary quadrature. The exact marginal horizon is recovered from the lag-corrected solution. The result gives the complete leading quasi-static near-zone response, exact in its radial dependence, for every admissible exterior datum within the specified massless overlap model.

Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling.

We present a recursive framework for computing arbitrary tree-level helicity amplitudes in the general effective field theory (EFT) of electromagnetism. We show that photon amplitudes can be constructed using a CSW-like recursion, whose building blocks consist of purely local subamplitudes. For a fixed number of external legs, only a finite number of these contact amplitudes need to be computed, and these admit compact expressions in terms of Hafnians. We further show that the contact amplitudes are encoded in an effective contact Lagrangian, that can be computed systematically from the general EFT Lagrangian using a suitable generating functional. We provide this contact Lagrangian up to $N=14$ photons. We argue that the contact Lagrangian reveals the hidden simplicity of helicity-conserving amplitudes, providing a simple proof of the equivalence between off-shell electromagnetic duality and helicity conservation. We further show how to resum the contact Lagrangian of a helicity-conserving theory to all $N$, and illustrate the procedure for Born-Infeld (BI) electromagnetism. Building on these methods and results, we compute the complete 6-point and 8-point tree-level helicity amplitudes generated by generic EFT operators, and the tree amplitudes up to 10-point in BI electromagnetism.

We study static extremal black holes in Einstein gravity coupled to a dilaton and two Maxwell fields with independent dilaton couplings $a$ and $b$. When $b=-1/a$ in four dimensions, a time-symmetric initial-value construction allows us to determine the masses and interaction energies of multi-black-hole configurations. On this special locus, the long-range force between any two extremal black holes vanishes. For arbitrary $a$ and $b$, a constant dilaton-shift symmetry, together with homogeneity and the extremality condition, yields a first-order ordinary differential equation that determines the extremal mass as a function of the two electric charges. This equation allows us to analyze the force between non-identical extremal black holes without having to know the explicit black-hole geometry. In all analytically controlled regimes that we examine, the locus $b=-1/a$ separates attractive behavior for $b>-1/a$ from repulsive behavior for $b<-1/a$. We extend the analysis to arbitrary spacetime dimensions, where the corresponding force-cancellation condition is $ab=-2(d-2)/(d-1)$. Finally, we test this sign pattern using the exact $A_2$, $B_2$ and $G_2$ Toda black holes. In the $G_2$ case, a potentially problematic branch is excluded because it contains naked singularities outside the horizon, suggesting an intriguing connection between regularity and the sign of long-range forces.

We study momentum-space correlators in minimal higher-spin gravity in $\mathrm{dS}_4$ using its holographic vector-model description. Connected $n$-point functions in this model are represented by three-dimensional one-loop integrals and are rational functions of the boundary kinematics. We show that the four-point function displays a nontrivial geometric feature: its physical singularity is governed by a Ptolemy relation for the dual momentum quadrilateral. At five points, the pentagon integral introduces an apparent leading Landau singularity, which we show is spurious and disappears once the Gram constraint is imposed. We derive a representation of the five-point function free of spurious singularities and organized in terms of graph-theoretic building blocks. We then verify the conformal invariance of these correlators and discuss their behavior in the soft, collapsed, and Ptolemy limits. This structure suggests a combinatorial bootstrap for higher-spin correlators at general multiplicity, in which conformal invariance and the physical singularities emerge from the underlying graph combinatorics.

The leading adiabatic response of a static black hole to a slowly evolving asymptotic modulus separates into a geometric problem and a functional-analytic one: the former identifies the tangent direction on the manifold of static solutions actually followed by the black hole, and the latter determines whether the resulting deformation admits a unique solution. We show that both can be characterized by explicit scalar criteria. Differentiating a smooth family of static solutions defines an intrinsic covector on its tangent space. When the family is parameterized by the asymptotic modulus and the static horizon-mass parameter, the kernel of this covector identifies a canonical tangent direction that coincides with the one selected by a slowly varying exterior modulus. Promoting the static family to a slowly evolving instantaneous representative does not solve the exact field equations; the resulting discrepancy defines a lag field governed, after elimination of the metric perturbations, by a single reduced radial operator. A representation convention separates the exact dynamical horizon from that of the instantaneous representative. A local slice then removes the remaining tangential ambiguity and induces a finite-rank perturbation of the reduced operator. The Fredholm index is preserved, and, whenever the finite-rank update is nontrivial, the canonical tangent zero mode is displaced from the kernel of the reduced operator. Under the transversality and Fredholm hypotheses, existence and uniqueness of the completed leading-order adiabatic boundary-value problem reduce to a single scalar matching condition on the resulting kernel generator. The construction depends only on a smooth non-extremal static solution manifold and the Fredholm properties of the reduced operator. A companion paper specializes the framework to the magnetic GHS family.

We determine the relative entropy of entanglement of a bipartite mixed state $\rho_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|\psi\rangle_{ABC}$, finding $E_R(\rho_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(\rho_{AB})$ and the mutual information $I(A:B)$. The upper bound is achieved by an explicit separable state obtained through one-sided Schmidt dephasing, which is therefore approximately closest.

Mirbabayi and Villadoro have provided strong numerical evidence for a universal upper bound on the mass of the lightest scalar field in gravitational Kaluza–Klein (KK) theories. This bound states that the lightest KK graviton, with mass $m_{1}$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{1})^2 \leq 4/3$. We give a proof of this bound using the approach of the conformal bootstrap applied to sum rules for massive spin-2 scattering amplitudes. We additionally show that each heavier KK graviton, with mass $m_n$, must couple to at least one scalar with mass $m_{\rm sc}$ such that $(m_{\rm sc} /m_{n})^2 < 36/25$.

We show that the tree-level amplitude for producing a monopole–antimonopole pair from an electrically charged pair cannot be constructed from the minimal one-photon couplings. Gluing the electric and magnetic three-point vertices gives a nonzero photon-pole contribution, but the resulting magnetic final state has the opposite discrete-symmetry eigenvalue from the electric initial state. Local four-point interactions cannot change the pole contribution fixed by the three-point couplings, so they cannot repair this mismatch. For fermions, the obstruction is specific to the minimal three-point coupling: an independent Pauli form factor supplies a spin-singlet three-point amplitude and allows the symmetry selection rule to be satisfied.