Papers

The supermembrane action is non-linear and a priori non-renormalizable. Still, some quantities in this theory may be free of log UV divergences and thus defined unambiguously. To explore this possibility we compute the energy of an M2 brane wrapped on a 2-torus in flat 11d space to two loops in the inverse-tension expansion. The result is free of logarithmic divergences and the same should hold also at higher loop orders. For fermions periodic around both circles the quantum corrections cancel, consistent with the BPS nature of the wrapped M2 brane state. For fermions antiperiodic around one or both circles the energy is a non-trivial function of the radii given by infinite sums of modified Bessel functions. We also compute 3-loop correction to the energy of the bosonic membrane on $\mathbb R^2\times S^1$. In contrast to the string case, it contains, besides powers of the 1-loop $\zeta(3)$ coefficient, a new term proportional to $\zeta(9)$. Summing contributions of all-loop bubble graphs leads to a simple cubic equation for the membrane energy. The analogous resummation in the Nambu or GS string case reproduces the familiar exact square-root expression ${\mathcal E}=\sqrt{(2\pi R\,T_1)^2+m_0^2}$. We find that the bubble-graph part of the membrane energy does not vanish for any value of the radius $R_{11}$. If contributions of other non-trivial diagrams in the supermembrane case do not qualitatively change this conclusion, this would disfavour the conjectured relation between 11d theory on an antiperiodic circle and the strong-coupling limit of type 0A string theory.

We calculate the dynamical tidal response coefficients (TRCs) of 2+1D analogue black and white holes generated by draining and fountaining bathtub flows, respectively. The parameter space is characterized by the frequency and azimuthal number of the Fourier modes and the rotation of the analogue black or white hole. In general, the TRC is a complex-valued function of these parameters. Its real and imaginary parts are defined as the tidal Love number (TLN) and the tidal dissipation coefficient (TDC), respectively. The TRC of the analogue black hole (ABH) exhibits several interesting features. At certain points in the parameter space, including the static case of vanishing perturbation frequency, the TLN exhibits logarithmic running, while the TDC vanishes. Unlike in Einstein gravity, fluid dynamics allows for the physical existence of an analogue white hole (AWH) event horizon. Time-independent, torque-free, barotropic, inviscid, axisymmetric fluid dynamical equations can yield a pair of transonic background flow solutions. The solutions in the pair, corresponding to an ABH-AWH pair, share the same angular momentum and Bernoulli constant but have opposite mass flow rates, all of which are conserved quantities. For such an ABH-AWH pair, the TRC of the AWH is the complex conjugate of the TRC of the ABH.

Light spectator fields provide a compelling inflationary origin for scalar dark matter, but their primordial fluctuations often generate excessive isocurvature perturbations on large scales. We develop a novel, exactly solvable filtering mechanism based on a tower of $\delta-$function contributions to the spectator mass, which we call kicks, whose dense limit converges to a smooth Coulomb-like profile. The filter produces a isocurvature spectrum during inflation that is strongly suppressed on large scales, rises with momenta as $k^3$ in the infrared, and, after a rapid turnover, smoothly approaches a constant plateau at small scales. This construction is motivated by a discrete translational invariance, admits an EFT regime in which radiative corrections can be systematically controlled, and can find a concrete realization in terms of an inflationary massive-clock model. We embed the filter in a minimal dark-matter scenario in which a spectator condensate oscillates about the minimum of a quadratic potential and behaves as pressureless matter. In this framework, the spectator dark-matter mass is directly related to the turnover scale of the inflationary isocurvature spectrum. We determine the resulting dark-matter abundance and analyze the relevant isocurvature and backreaction constraints. The most restrictive realization, in which the spectator condensate is generated during inflation, favors a relatively low inflationary scale.

We investigate the critical exponents $(\gamma,\nu)$ at the current-driven tricritical point (TCP) associated with chiral symmetry breaking in a nonequilibrium steady state described by the D3/D7 model. In the symmetry-broken phase, we find that, unlike in the conventional Landau theory, both $\gamma$ and $\nu$ can take values different from those predicted by the Landau theory and depend on the path along which the TCP is approached in the phase diagram. However, when the TCP is approached with the ratio of the effective temperature to the heat bath temperature, $T_{*}/T$, held fixed, the critical exponents agree with those of the Landau theory. These results suggest that the critical phenomena at the current-driven TCP may be described by the Landau theory along the $T_{*}/T$-fixed line, whereas a nontrivial extension of the Landau theory is required for a more general description of the critical phenomena along arbitrary paths.

We study perturbative anomaly inflow for effective theories supported on orbifold fixed loci of the internal geometry. Donnelly's equivariant APS theorem gives a fixed-point density, whose degree-$(d+2)$ component is identified as the anomaly polynomial of the $d$-dimensional effective theory. We apply the construction to six-dimensional A-type orbi-instanton theories engineered by $N$ M5-branes probing a transverse $\mathbb{C}^2/\mathbb{Z}_k$ singularity at an end-of-the-world M9-brane. For a flat $E_8$ connection specified by $\rho:\mathbb{Z}_k\to E_8$, we compute the non-identity ALE fixed-point class on the M9 wall. Its degree-eight component agrees with the complete Kac-label-dependent remainder conjectured in \cite{MOTZ} by Mekareeya-Ohmori-Tachikawa-Zafrir, including the $SU(2)_R$ and tangent-bundle curvatures. Together with the known M5/Hořava–Witten and ALE/Hořava–Witten terms, this reproduces the unflavored tensor-branch anomaly polynomial. This local equality further suggests a complete M-theory corner-inflow interpretation. The same prescription also be extended to include flavor symmetries as the centralizer of $E_8$.

At leading order in the genus expansion the ETH matrix model for DSSYK reproduces its correlators by construction, while its higher-genus corrections are conjectured to capture higher-topology contributions in the dual sine-dilaton gravity – a correspondence established so far only for the disk and the wormhole. At fixed genus the correlators are built from discrete volumes $N_{g,n}$, polynomial in $q$-deformed zeta values $\zeta_q(2k)$ with $q=e^{-\lambda}$, $\lambda$ being the DSSYK coupling. These lie in the ring of quasimodular forms generated by the Eisenstein series $E_2,E_4,E_6$, whose $S$-duality yields an exact closed form for the leading non-perturbative correction as $\lambda\to0$, controlled by $\widetilde q=e^{-4\pi^2/\lambda}$. Known at disk level, this scale is shown here to govern the fixed-genus, higher-boundary amplitudes as well. We show that the term linear in $\widetilde q$, at leading order in $\lambda$, is captured entirely by the $q$-deformed Weil–Petersson volumes, and reduces to a finite sum of intersection numbers of $\kappa$-classes on the moduli space $\overline{\mathcal M}_{g,n}$ of stable curves, computable without repeating the topological recursion that produced the $N_{g,n}$. We tabulate it for every $(g,n)$ whose $q$-deformed volume is known in closed form, and extend it to $(3,1),(3,2),(4,1)$, where none is available. The construction is not restricted to leading order: we work out $O(\widetilde q^2)$ for the same cases.

Primordial non-Gaussianities are at their largest when the curvature perturbation is coupled to a massive field by a mixing too strong to be treated perturbatively. We show that this regime, naturally reached in multifield inflation, is solved analytically by the Laplace-space representation we recently introduced, in which every mode becomes a superposition of plane waves weighted by a single kernel. The bispectrum then follows as a rapidly convergent series of elementary functions, in perfect agreement with independent numerical results. We find that the cosmological collider signal at strong mixing is larger than widely believed, with only half of the usual Boltzmann suppression. Its amplitude further grows with the number of time derivatives of the curvature perturbation in the interaction, singling out the most promising observational targets.

Motivated by the old idea of treating gravity as a gauge theory, we review the gauge-theoretic construction of Conformal Gravity and of Noncommutative (Fuzzy) Gravity. We then outline how these gauge formulations of gravity can be unified with internal interactions described by an SO(10) Grand Unified Theory, based on the critical observation that the dimension of the tangent-space symmetry group of a curved manifold need not coincide with the spacetime dimension.

We propose an extension of AdS/CFT in which quantum gravitational wavefunctions of connected bulk geometries are assembled into a Fock space of universes. Splitting and joining interactions in a third-quantized Hamiltonian then provide a quantum description of changes in bulk connectivity and topology. Reduced phase-space quantization supplies the physical one-universe Hilbert space and a radial Schrödinger evolution with respect to which the topology-changing interactions are ordered. We develop the construction concretely in AdS$_3$ gravity with a torus boundary, where these ingredients can be described explicitly. The light spectrum is treated as fixed, non-normalizable background data, whereas the normalizable states above the black-hole threshold are quantized as dynamical modes. A conventional boundary theory is selected by choosing a coherent state whose universe-field expectation value, together with the fixed background contribution, yields consistent CFT data at the asymptotic boundary. Generic one-universe wavefunctions need not admit such an interpretation. This raises the possibility that CFT-realizable wavefunctions are nongeneric in the gravitational state space and are not closed under arbitrary superpositions of gravitational states. The known two-torus spacetime-wormhole amplitude, which lies at the heart of the factorization problem, provides concrete input for the topology-changing interactions of the third-quantized theory. A complementary cutting-and-gluing description yields an effective ensemble interpretation when the resulting gravitational sectors admit consistent boundary-theory interpretations, without assuming a fundamental ensemble of boundary theories. We also discuss replica wormholes and baby-universe processes within the same framework.

In the present paper, the cases of a uniformly accelerated reference frame and a Schwarzschild black hole in two and four dimensions are discussed focusing on formal aspects of the corresponding quantum scalar field theories. The main emphasis is made on building consistent quantum field theories and highlighting the problems that are not considered elsewhere. In particular, some pathologies in the case of a uniformly accelerated reference frame are discussed in detail: it is shown that some quantum states that are well defined in Minkowski spacetime possess an infinite energy when considered in Rindler spacetime. In the case of a Schwarzschild black hole in four dimensions, it is shown that the standard theory providing the Unruh vacuum state turns out to be inconsistent. The problem of consistency of quantum scalar field theory in Kruskal-Szekeres spacetime is also discussed.

The large-scale dipole anisotropy observed by the Pierre Auger Observatory above $8$~EeV provides important clues about the origin of ultra-high-energy cosmic rays (UHECRs). In this work, we investigate whether gamma-ray active galactic nuclei (AGNs) from the Fermi-LAT Fourth AGN Catalog (4LAC) can explain the observed dipole and examine the contribution of nearby starburst galaxies (SBGs). Incorporating source fluxes, redshift distributions, GZK attenuation, and a mixed-composition framework, we demonstrate that single-source populations of AGNs and SBGs alone fail to reproduce the observed Auger dipole. To resolve this, we construct a hybrid AGN+SBG model. The best-fit solution for the $8$–$16$~EeV interval requires a $23$% AGN contribution and $45$% SBG contribution, which gives a dipole amplitude of $5.03$% while maintaining the dipole direction of ($104.1^\circ$, $-25.1^\circ$) with angular separation of $7.10^\circ$. In the other energy intervals also, we find that the nearby SBGs increasingly dominate the anisotropic component while AGNs provide a subdominant contribution alongside a quasi-isotropic background.

Tidal deformability provides a sensitive probe of the structure of compact objects, and black holes are exceptional in having vanishing static Love numbers in four-dimensional Einstein gravity. We ask what happens to this fine-tuned rigidity across the black hole-string transition, where the same states are expected to admit a weakly coupled description as a self-gravitating highly excited string, or "string star". We compute the static tidal Love numbers of the Horowitz-Polchinski (HP) string star for multipoles $\ell=2,3,4$ in $D=4,5,6$. The response is non-zero in all cases, as in the available $\alpha'$-corrected black hole results, so the zero-Love structure of four-dimensional Einstein gravity does not survive on either side of the transition. On the string side, however, the response has a distinctive multipolar structure: the Love numbers grow rapidly with $\ell$, and we show analytically that this growth originates from the competition between the multipolar weight of the tidal field and the exponential tail of the winding condensate, with the result that the radial scale probed by the deformability grows linearly with $\ell$ at large multipole number. This provides a direct tidal signature of the extended, surface-less nature of the string star. We discuss the comparison with $\alpha'$-corrected black holes and the limitations of the currently available perturbative results at large $\ell$.

In this paper, we study the renormalization of a three-dimensional quartic model on a compact connected Riemannian manifold with a boundary. We show that, in addition to the standard shift of the mass parameter, it is necessary to take into account boundary contributions involving singular coefficients. This indicates the need to extend the classical action within the framework of standard renormalization theory. The requirements of consistency regarding the gluing of manifolds lead to renormalization of an operator on the boundary.

We present a study of quasielastic lepton-nucleus scattering within the local density approximation, using ab initio spectral functions from infinite nuclear matter derived with self-consistent Green's functions theory and interpolated by neural networks. We include final-state interactions in terms of the particle spectral function and investigate the importance and range of validity of this treatment for varying momentum transfer. The performance of the model is tested for inclusive electron scattering on different isospin-symmetric target nuclei, and we present results for $^{12}$C, $^{16}$O, and $^{40}$Ca. Theoretical uncertainties originating from the neural network interpolation and the Hamiltonian dependence are assessed. We also present a calculation of charged-current responses of $^{16}$O and the flux-averaged total $\nu_\mu-^{12}$C cross section. Our model shows good agreement with experimental data within the range of validity of our approximations. The framework can be readily extended to include additional dynamical mechanisms, such as pion production, as well as other nuclear Hamiltonians.

Locality and unitarity are fundamental principles of quantum field theory. For tree-level scattering amplitudes, locality determines which propagator poles may occur together, while unitarity fixes their residues through factorization. Previous uniqueness theorems have repeatedly shown that unitarity can emerge from locality combined with other physical principles. In this Letter we give the first complete all-multiplicity proof for the emergence of locality in this setting. We focus on Tr($\phi^3$) theory and phrase locality as a problem in geometric combinatorics. Planar propagators are chords of a polygon, and a denominator is local exactly when its chords triangulate the polygon, and non-local otherwise. We show that hidden zeros—regular kinematic conditions on which the amplitude vanishes—enforce pole compatibility and therefore imply a local singularity structure. The proof rests on two ingredients: a graphical star test determines when a chosen zero eliminates a pole product, and a smoothing procedure finds such a zero. Thus, once the planar pole alphabet and denominator bound are specified, locality and unitarity emerge together from a single on-shell principle: hidden zeros. Equivalently, our proof provides a novel characterization of a familiar concept: polygon triangulations are precisely the chord configurations that evade every star test.

At a deeper level the principle of least action is interpreted as the law of least entropy increase consistent with Prigogine's principle of minimum entropy production, and the implications of quasistatic information quantization rule (Proc. R. Soc. A 480: 20240024), are explored for the conjectured second law of quantum complexity. It is thus shown that the conjectured second law of complexity is derivable from the information quantization rule such that long after heat-death the quantum state complexity evolves as $C(t)=C_{\rm max}\exp(-1/t)$, increasing with time to a saturation value $C_{\rm max}$ that is exponential in the equilibrium entropy $S_{\rm max}$. For the out-of-equilibrium circumstances, however, the quantum complexity can decrease with the time, asymptotically tending to a minimum determined by the distance from equilibrium.

We study cosmological perturbations in multi-field inflation in which the scalar fields couple to the Gauss-Bonnet terms through a general coupling function $f(\phi^a)$. We derive the complete quadratic action for the field perturbations in spatially flat gauge and find that, besides corrections to the kinetic, gradient and mass matrices, the Gauss-Bonnet coupling induces an antisymmetric velocity coupling that vanishes in Einstein gravity. Decomposing the field perturbations into curvature and isocurvature modes, we show that the effective mass of the curvature perturbation and the non-derivative mixing mass vanish identically, $\mathcal{M}_{\mathcal{R}}^2 = \mathcal{M}_{\rm mix}^2 =0$ which are justified by the Weinberg's adiabatic mode. We then compute the curvature power spectrum in two limits. First, when the isocurvature mode is heavy, it can be integrated over all scales. This yields an effective single-field theory of the curvature perturbation with a modified sound speed. Second, when the gradient of the coupling function is aligned with the background trajectory ($f_N =0$), the derivative mixings disappear and the superhorizon transfer of isocurvature into curvature perturbations is governed by the turn rate, which is modified by the Gauss-Bonnet corrections. We also present the tensor power spectrum and the tensor-to-scalar ratio at linear order in the coupling.

These lectures provide a pedagogical introduction to the study of finite-$N$ physics of the AdS/CFT correspondence. More specifically we develop the consequences of the trace relations for the space of gauge invariant operators, using powerful methods from invariant theory. Our key conclusions are \begin{itemize} \item that the complete set of trace relations can be solved, leaving a non-redundant set of gauge invariant operators, \item that this non-redundant set can be generated using two types of generators, called primary and secondary invariants, and \item that the primary invariants acquire a natural interpretation as perturbative gravitational degrees of freedom, while the secondary algebra encodes non-perturbative effects of the dual gravitational theory. \end{itemize}

We provide a geometric foundation for the kinetic theory of photons. Although the induced metric $\hat h$ on the light cone bundle $\Gamma_0^+$ is degenerate, which causes the corresponding volume element to vanish, we can still use a method similar to the Hodge dual to construct a volume element $\eta_{\Gamma_0^+}$ for the light cone bundle. Based on this geometric structure $(\Gamma^+_0,\eta_{\Gamma_0^+},\hat h)$, we establish the fully covariant Boltzmann equation for photons. More importantly, the volume element and the induced metric are linked in a nontrivial way, which allows the physical distributions to be defined consistently. This yields the corresponding hydrodynamic quantities and their divergences, which take the same form as in the case of massive particles.

We investigate the cosmological evolution of a spherical brane within the shellworld (dark bubble) scenario embedded in a five-dimensional charged AdS bulk spacetime. For zero or small value of the brane cosmological constant, the shellworld universe has a nonsingular bouncing and cyclic nature with the bounce induced by the charge parameter of the bulk spacetime. On large value of the brane cosmological constant, the shellworld undergoes a nonsingular bounce and expands eternally. Under certain conditions, the brane bounces outside the bulk horizons, leading to a geometrical resolution of the Cauchy horizon instability present in standard braneworld models. Furthermore, analysis of linear scalar perturbations reveals that test scalar field modes remain regular and non-divergent across the bounce. Finally, we incorporate uniformly distributed long strings in the bulk and demonstrate that the bounce still persists while avoiding the horizon instability.

We propose a new way to probe elliptic small-$x$ gluon geometry in hard diffractive dijet deep inelastic scattering: a localized lepton wave packet carrying orbital angular momentum is used as a tunable transverse analyzer of the target. Unlike the conventional plane-wave setup, where the probe provides a fixed transverse projection, the OAM mode supplies additional radial and azimuthal structure while leaving the target dipole matrix element unchanged. We characterize the resulting elliptic response through $S_M=D_M-C_M$ and find finite-yield response nodes whose origin depends on the OAM channel. In the present benchmark, the $M=1$ crossing is associated mainly with a zero of the direct response, whereas the $M=3$ channel exhibits a nontrivial cancellation $D_3=C_3\neq0$. Signed transverse response densities show that this node results from a spatial cancellation rather than from a disappearance of the underlying scattering strength, and its position can be shifted by changing the beam–target offset. The specific sensitive value of $M$ depends on the analyzer profile and kinematics; the broader result is that localized OAM wave packets provide a controllable probe-side degree of freedom for small-$x$ gluon tomography.

We study the one-loop relation between an effective-field-theory extension of Poincaré gauge theories of gravity with propagating torsion and its unimodular counterpart. In the Einstein representation, we consider two representative quadratic torsion subsectors, namely totally antisymmetric (axial) torsion and the vector component of hook-antisymmetric torsion. On maximally symmetric metric backgrounds with vanishing background torsion, the diffeomorphism-invariant and genuine unimodular theories yield identical one-loop determinants in both sectors, reproducing the same local logarithmic divergences. We further examine flat backgrounds with homogeneous axial or vector torsion, where metric-torsion mixing is present. In each case, the torsion-dependent one-loop effective action in unimodular gauge and in the genuine unimodular formulation is controlled by the same physical determinant. Thus, for the actions and backgrounds considered, the unimodular constraint does not modify local one-loop torsion dynamics. We also delineate the limitations of this equivalence and the extensions needed for generic torsionful curved backgrounds.

We derive the rank-two string-Carroll limit of the canonical stress–spin Ward system for probe matter on a fixed torsion-free background. Beyond rank-one Carroll spin hydrodynamics, this retains the coupled Riemann–spin force, a second longitudinal momentum projection, and the longitudinal boost bivector allowed only by a two-dimensional longitudinal kernel. We first extract the term linear in an independent spin amplitude $\varsigma$ and then expand in the near-horizon parameter $\lambda=\epsilon^2$, avoiding contamination by the omitted $\mathcal{O}(\varsigma^2)$ thermodynamic spin feedback. For finite mixed stress and $S^{\lambda\mu\nu}=\mathcal{O}(\varsigma\epsilon^p)$, $p=0$ is the unique sector in which the induced stress and curvature source balance at the first generic Ward order. On the regular branch of a smooth nonextremal static spherical outer horizon, locally normalized longitudinal and transverse spin amplitudes obey the same dilution law, while the curvature force first appears at $\mathcal{O}(\varsigma\lambda^2)$. For a general barotrope, the stationary system reduces to one thermodynamic quadrature and one local inverse. For the affine constant-sound-speed family $p=\alpha\mathcal E+\Pi$, $0\leq\alpha<1$, we obtain an explicit closed-form parametric solution, leading profiles for both spin channels, and fixed-radius, linear-spin corrections to enthalpy, pressure, and rapidity away from the sonic point. The response is governed by $\mathcal R^{(L)}_h=(f_2+3f_1\psi_1)/2$ and the longitudinal spin flux. We prove that the stationary closed-sphere Killing flux is invariant under regular pseudo-gauge improvements. In Reissner–Nordström, the response vanishes at the radial-tidal inversion $|Q|/M=2\sqrt{2}/3$; in the Einstein–Maxwell–dilaton family, its zero is $R_-/R_+=(1+a^2)/2$ for $0\leq a<1$. The Frenkel limit removes this response and the longitudinal boost sector.

We comment on an error in the charged quark star literature ( Phys. Rev. D, 102(3):034031, 2020 ) that resulted in erroneous solutions to the radial stability equations for charged interacting quark stars in ( Phys. Rev. D, 104(12):123007, 2021 )[2]. In this comment article we recalculate the fundamental radial eigenfrequencies for charged, interacting quark stars in general relativity and discuss any departure from previous results [2]. Most of the qualitative trends persist, but the magnitudes of the separation between the maximum mass and stability points on a given branch can change significantly. We also note that all branches in [2] that contained no stable solutions now have stable solutions in their corrected counterparts. The net effect is that in all of the studied cases charged quark stars have a greater range of stability than originally predicted. We also compare four recent observational constraints not included in previous studies, and find that these constraints are satisfied by a subset of the mass-radius relations we obtain.

We consider $(3+1)$-dimensional asymptotically locally (anti-)de Sitter ((A)dS$_4$) spacetimes with boundary conditions allowing for gravitational flux. We construct an infinite tower of higher-spin charges as perturbative solutions in the cosmological constant $\Lambda$ to a hierarchy of evolution equations resulting from an asymptotic expansion of the Einstein equations. We show that these charges canonically realize the $\Lambda$-deformed $w_{1+\infty}$ algebra ($L_{\Lambda} w_{1+\infty}$) on a restricted gravitational phase space, thereby extending the higher-spin symmetry structure of asymptotically flat spacetimes to asymptotically (A)dS spacetimes. We further construct the curved-space counterparts of conformally soft gravitons directly in terms of spacetime data. We show that they are primaries with respect to an $\mathfrak{sl}(2,\mathbb{R})$ subalgebra of the (A)dS$_4$ isometry algebra and that their Poisson brackets with the quadratic higher-spin charges reproduce the $\Lambda$-deformed celestial operator product expansion proposed by Taylor and Zhu. Our results establish the bulk gravitational origin of the $L_{\Lambda}w_{1+\infty}$ symmetry and extend the celestial bulk-boundary dictionary to asymptotically (A)dS$_4$ gravity.

In particle physics the virtual N$^3$LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. For gluon-fusion $gg\!\to\!H$ we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the $\overline{\mathrm{MS}}$ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit $E_M\!\to\!\infty$.

In this work, we analyze the late-time two-point correlation function in Jackiw–Teitelboim gravity, focusing on the genus-two ($g=2$) contribution associated with two baby universes. Extending the analysis of the single-baby-universe ($g=1$) case, we formulate an amplitude describing the emission and absorption of two baby universes during the evolution of the Hartle–Hawking state. This formulation reduces the problem to a moduli-space integral involving the Weil–Petersson volume $V_{0,3}$. To evaluate this integral, we decompose $V_{0,3}$ into contributions from Kontsevich graphs and extend the no-shortcut condition to the relevant genus-two strip geometries. Combined with the strip approximation, this decomposition reorganizes the moduli-space integral into a finite sum of contributions associated with distinct geometric configurations. We then explicitly evaluate the strip-geometry contributions corresponding to the emission of two baby universes and determine their contribution to the genus-two late-time two-point correlation function. Our results suggest that the strip approximation, together with the no-shortcut condition, provides a useful analytic framework for studying higher-genus geometries containing multiple wormholes.

We study supersymmetric near-horizon geometries of gauged $D=5$ supergravity coupled to vector multiplets, on the branch where the canonical rotational Killing vector $\tilde V$ of the cross-section ${\cal S}$ is non-vanishing. No rotational symmetry is assumed, and nothing about the set where the frame built from the Killing spinors degenerates. On a compact connected ${\cal S}$ without boundary a second rotational Killing field, independent of $\tilde V$, always exists and is an isometry of all of ${\cal S}$. Where the moduli vary it is $$ U_i=\parallel\eta_-\parallel^2\big(\alpha Z_i-\epsilon_{ijk}Z^ju^k\big) , \qquad u_i=\Phi P_i-h_i , $$ a polynomial in the horizon data, hence smooth everywhere; where the moduli are constant the horizon is locally homogeneous. The only further hypothesis for these results is that the superpotential $\Phi=\chi V_IX^I$ is nowhere zero — weaker than the non-negativity of the scalar potential assumed in the earlier literature. The two sub-branches are separated by $K=Q_{IJ}C^IC^J$, which vanishes exactly in the minimal theory: $K\equiv0$ recovers the result of Grover, Gutowski, Papadopoulos and Sabra, while elsewhere $K>0$ and $\alpha$ is either identically zero or nowhere zero. Each of $K\equiv0$, $P\equiv0$ and $P\not\equiv0$ occurs on compact ${\cal S}$. Constant moduli return the local geometries of Kunduri and Lucietti as a conclusion, not an ansatz. Varying moduli with $\alpha\not\equiv0$ give a cohomogeneity-one $T^2$ action whose orbit space is a closed interval, so ${\cal S}$ is $S^3$, a lens space or $S^1\times S^2$; the last is excluded by two global first integrals, a new one, $\alpha\parallel\eta_-\parallel^4$, and the constant spinor norm already known. A varying-moduli supersymmetric $AdS_5$ black ring therefore cannot exist with $\alpha\not\equiv0$; the $S^1\times S^2$ window survives only at constant moduli or at $\alpha\equiv0$.

In a thermodynamic environment, thermal field theory (TFT) describes a large ensemble of interacting particles. This may appear to be the same as in classical statistical mechanics. Therefore, we study the scalar propagator and fermion propagator by considering an arbitrary parameter $\sigma$ that allows for a path integral description in real-time formalism (RTF). We constructed those propagators which allowed us to know how particles moved from one point to another point in momentum space as well as in mixed space, at finite temperature without a chemical potential.

We investigate geometric structures defined by 4-forms, encompassing important classes of geometric structures with torsion including almost Hermitian, $\mathrm{G}_2$, $\mathrm{Spin}(7)$, and almost quaternion/hyper Hermitian. Within this unified framework, the underlying 4-form naturally determines geometric data that define a string algebroid over the manifold. In particular, it gives rise to a canonical notion of instanton, thereby linking these geometries to gauge-theoretic structures in generalized geometry and heterotic string theory. We further prove that these data induce generalized Ricci-flat metrics. Finally, we examine the main examples in the literature and construct several explicit ones.