Papers

Asymptotic equivalence between the quasi-Grammian and quasi-Wronskian representations of $N$-soliton solutions in the $J$-matrix formulation of the anti-self-dual Yang-Mills (ASDYM) equation is established up to a constant matrix factor. This formulation, known as the Yang equation, serves as the equation of motion of the four-dimensional Wess-Zumino-Witten (WZW$_4$) model and is equivalent to the ASDYM equation. To visualize the solitonic behavior, the action density of the WZW$_4$ model is evaluated for $\mathrm{G}=\mathrm{U}(2)$, demonstrating that the quasi-Grammian and quasi-Wronskian representations exhibit the same asymptotic soliton profiles, while the phase shift factors associated with $N$-soliton collisions are obtained explicitly. Hence, by virtue of the particle-like nature of solitons, the two representations describe the same class of ASDYM $N$-soliton solutions. These solitons can be regarded as a four-dimensional analogue of KP/KdV-type multi-solitons in fluid dynamics, suggesting a possible connection between the ASDYM equation and higher-dimensional Sato theory. Exact quasi-Grammian $N$-soliton solutions are also presented for $N\leq4$.

Relativistic quantum field theory is the structure on which the Standard Model and beyond-Standard Model physics are built. One of its most striking predictions is the Unruh effect: an observer undergoing uniform linear acceleration measures the Minkowski vacuum as a thermal bath at a fixed temperature. Despite decades of theoretical interest, this effect has never been directly observed. We propose to use the high acceleration gradients provided by wakefield accelerators, coupled with a forward laboratory-frequency ~THz detector array, to measure the resulting forward-beamed radiation, and outline the unique signature provided by quantum detailed balance to extract the signal from backgrounds. While challenging, such a measurement appears within reach of present-day accelerator and detector technologies.

We build an ultralight dark matter model with repulsive self-interactions, starting from a 5D action that only includes a $U(1)$ gauge field and several massive and charged free fermions. The dark matter scalar field corresponds to the fifth component of the gauge field, after compactification to 4D. Although the single-fermion case only leads to attractive self-interactions, two fermions can already give rise to repulsive self-interactions, thanks to a Scherk-Schwarz twist around the fifth dimension. We check the observational and theoretical self-consistency of this scenario, from the inflation stage to the current time. We find that large ranges of model parameters are allowed. For scalar masses below $10^{-12}$ eV the self-interactions are negligible and the model behaves as fuzzy dark matter. For higher masses the repulsive self-interactions govern the formation of solitons of astrophysical size. Larger sizes require a large initial misalignment or small masses in the fuzzy dark matter regime.

We investigate the holographic temporal entanglement entropy of a boosted \((1+1)\)-dimensional plasma within the AdS\(_3\)/CFT\(_2\) correspondence, considering a Lorentz-boosted BTZ black hole background. We solve the coupled extremal-surface equations analytically and obtain a closed-form expression for the HTEE. Our results show that the real part of the SHTEE depends on the velocity, whereas the imaginary part is independent of the velocity and remains constant and universal. The known static BTZ result is recovered in the zero velocity limit, as expected.

We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting the global formulation of generalized topological recursion, we establish a contour deformation of the recursive residue formula that replaces contributions from these essential singularities by residues at meromorphic points. This provides a natural recursive framework for exponentially ramified spectral curves while remaining entirely within the generalized topological recursion formalism. Our formalism can also be viewed as a limiting case of the Bouchard-Eynard higher-order topological recursion, obtained when the order of a ramification point tends to infinity in a convergent manner, as occurs, for example, for exponential singularities while $dy$ remains regular and non-vanishing. We further illustrate the resulting formalism through several examples, including transcendental functions and the $x$-$y$ dual of the Mirzakhani curve.

This study investigates the dynamical behavior of particle's test around a spinning charged Einstein-Maxwell-dilaton (EMd) quantum corrected black hole (QCBH) by examining the effects of spinning parameter $a$, quantum correction parameter $b$, and charge parameter $Q$. Using EMd spacetime geometry, we analyze the effective potential and effective force to determine the stability and structure of the circular orbits in a strong gravitational field. Furthermore, we calculate the oscillation frequencies radial $(\Omega_r)$, vertical $(\Omega_\theta)$, and angular $(\Omega_\phi)$, as well as the corresponding Periapsis and Lense-Thirring precession frequencies. The spin parameter primarily determines the spinning properties of spacetime, while the quantum correction and charge particle introduce additional biases to Kerr-Newman geometry, particularly near the event horizon. These corrections alter the position and stability of the circular orbits, and the spectrum effectively associates with particle's motion. The results provide a comprehensive description of the orbital dynamics of spinning EMd QCBH through future high-precision astrophysical observations.

A hypercomplex formulation of scalar electrodynamics is developed, in which dissipation emerges as an intrinsic dynamic property dictated by the extended local gauge symmetry U(1)XSO(1,1). By constructing an effective free-energy functional, we derive the generalized Ginzburg-Landau equations and analyze the thermodynamic stability of the system. Our analysis of the vacuum state up to the fourth order reveals that the constraint on the coefficients associated with the invariants prohibits the coexistence of mixed states, formally establishing the existence of a bicritical point. Consequently, upon crossing the critical temperature, the system is forced to undergo a discontinuous first-order phase transition. Furthermore, we demonstrate that the hyperbolic symmetry induces a structural instability when the effective quartic couplings take negative values, rendering the free energy unbounded from below and creating asymptotic directions of instability.

We give the colour-singlet eigenvalue of the three-loop BFKL kernel of planar N=4 super Yang-Mills in closed form at odd conformal spin n. It splits into a holomorphic block and its conjugate, chi_2(n,nu)=(1/4)[F_n(z)+F_n(zbar)] with z=(|n|-1)/2+i nu, and the block is a finite combination of nested harmonic sums of one variable, rational functions and transcendental constants, of uniform transcendental weight five. At the two lower orders the sums are evaluated at the two conjugate points only. At three loops they are evaluated at every point of the integer ladder running from the reflected endpoint -zbar up to z, and one step beyond it, and for all but seven of the slots the coefficient at each rung is fixed by the two distances to the ends. Summing over the one-variable functions before summing along the ladder replaces the rules of those slots by one function of one variable under each ladder weight. The remaining seven are carried by a sum along the ladder whose summand moves with the summation index. All forty-seven coefficient slots follow from rules uniform in the conformal spin at every odd n>=3, with no per-spin coefficient tabulated in the definition; the n=1 boundary block is supplied separately. Those rules are a reconstruction from the computed spins, exact at every one of them, verified over the range n<=99 and at the holdout spin n=101, and not proved at arbitrary odd n. Along nu=0 the intercepts agree with the Quantum Spectral Curve values at every computed odd spin through n=91. That comparison tests the three-loop integrand and the reduction performed here together, at one point of each spin, and for most of those spins it is the first comparison of its kind.

We give the next-to-next-to-leading order color-singlet BFKL eigenvalue of planar N=4 super Yang-Mills at odd conformal spin n in closed form. At the two lower orders the known expressions contain nested harmonic sums only at the two conjugate points z=(|n|-1)/2+i nu and zbar. At three loops the sums are evaluated on a ladder of integer-shifted arguments from the reflected point -zbar up to z, with one point past it, the coefficient at a rung fixed by its two distances to the ends. Seven families are the exception, their coefficients written through ladder sums whose summand shifts with the summation index. For one of the seven the coefficient lies outside the fixed-coefficient algebra of nested harmonic sums of the two distances, an arithmetic obstruction in the denominators. That exclusion reaches the eigenvalue coefficient only through an agreement of rule and coefficient verified and not proved. Rules uniform in the conformal spin produce all forty-seven families at every odd n>=3; no per-spin coefficient is tabulated in the closed form, and the n=1 boundary block is supplied separately. Those rules are a reconstruction from the computed spins, exact at every one of them, verified over the range n<=99 and at the holdout spin n=101, and not proved at arbitrary odd n. Each atom-table coefficient is a rational combination of 1, pi^2 and zeta_3, coefficient and atom together carrying transcendental weight five. Along nu=0 the intercepts match the Quantum Spectral Curve values at each computed odd spin through n=91, the extent of those values. The comparison tests the integrand and the reduction together at one point of each spin, for most of them for the first time. Away from that line the closed form gives the collinear behavior of the block uniformly in the spin, which the intercepts alone do not fix.

This publication consists of slides from my talk at the Simons Center for Geometry and Physics in 2024. It contains a brief review of the L-functional formalism, along with a discussion of its possible applications to QED, linearized gravity, and quenched disorder. The most interesting part is the discussion of the infrared problem in QED and a conjecture on how to construct an infrared-finite perturbation theory for QED.

In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale \(E_M\). By using the direct clock-energy channel, we find conservative lower bounds on \(E_M\) at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time–energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality. We explore the idea of using a squeezed-state experiment with the $^{229}\mathrm{Th}$ nuclear clock to test the time–energy structure of nonlocal quantum field theory. The idea is reasonably obtainable within the near future of nuclear clock experiments. One would prepare an ensemble of thorium nuclei in a coherent superposition of the nuclear ground state and the low-lying isomeric clock state, entangle the participating nuclei through a collective interaction, and generate a family of spin-squeezed states with a tunable squeezing parameter $r$. Then a phase-controlled analysis pulse will rotate the selected collective nuclear quadrature into a measurable ground-isomer population difference. Near a strongly polarized collective state the normalized operators $J_y/\sqrt{S}$ and $J_z/\sqrt{S}$ obey the same approximate canonical algebra as the phase and amplitude quadratures of a squeezed optical mode. We use this experiment to either probe or bound the nonlocal energy scale $E_M$.

We investigate the generation and propagation of gravitational waves in the leading parity-even infrared truncation of Hořava-Lifshitz gravity, characterized by the modified tensor dispersion relation $\omega^{2}=k^{2}+\alpha k^{4}$. Working in the transverse-traceless sector, we show that the higher-spatial-derivative correction preserves the conventional plus and cross polarizations and introduces neither polarization mixing, helicity splitting, nor gravitational birefringence. We construct the retarded Green function of the modified wave operator and derive the radiation-zone waveform to first order in $\alpha$. The resulting signal exhibits a frequency-dependent amplitude renormalization together with a dispersive propagation phase that accumulates over the source-observer distance. We apply the formalism to a binary black hole system in a quasi-circular orbit and obtain the polarization waveforms for an arbitrary observation direction. We further derive the corresponding energy flux, total luminosity, and adiabatic chirp evolution. In terms of the observed gravitational wave frequency $f$, the leading corrections satisfy $\Delta h_{A}/h_{A}^{\mathrm{GR}}=-8\pi^{2}\alpha f^{2}$ and $\Delta P/P_{\mathrm{GR}} =\Delta\dot{f}/\dot{f}_{\mathrm{GR}} =-16\pi^{2}\alpha f^{2}$, while the accumulated generation phase has the frequency dependence of a relative third post-Newtonian contribution. By mapping the Hořava-Lifshitz coefficient to the LIGO-Virgo-KAGRA modified-dispersion parametrization, we obtain $-6.2\times10^{2}\,\mathrm{eV}^{-2} <\alpha< 1.9\times10^{2}\,\mathrm{eV}^{-2}$ at $90\%$ credibility from the GWTC-4.0 posterior.

We demonstrate that in a scalar-tensor theory where dark matter is conformally coupled to a scalar field, a black hole surrounded by a Hernquist dark matter halo can undergo spontaneous scalarization, acquiring a nontrivial scalar field configuration. The astrophysical properties of the dark matter halo directly dictate the quantum-like spectrum of scalar field configurations around the central black hole. Remarkably, the conformal coupling constant becomes discretized and is determined solely by the halo's compactness parameter.

We investigate colored $\Delta_T$ noise, i.e., finite-frequency $\Delta_T$ noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored $\Delta_T$ noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since $\Delta_T$ noise is driven solely by a temperature and voltage bias under zero average charge current conditions, it eliminates current-induced Joule heating and directly probes intrinsic thermal fluctuations. We show that chiral, spin-conserving helical, and spin-flip helical (trivial) EMs exhibit distinct colored $\Delta_T$-noise signatures under appropriate bias protocols. Incorporating energy-dependent scattering through a quantum point contact, we demonstrate that electron-hole asymmetry significantly modifies the finite-frequency spectrum while preserving these distinguishing features. Notably, colored $\Delta_T$ noise exhibits a frequency-dependent sign reversal absent in the corresponding white ($\omega=0$) $\Delta_T$ noise. We further investigate zero-temperature colored quantum shot noise and find that it vanishes identically for chiral EMs, whereas the spin-conserving helical response changes sign with frequency. By contrast, spin-flip helical (trivial) EMs exhibit a positive colored shot-noise spectrum. However, the corresponding colored $\Delta_T$ noise retains its characteristic sign reversal, providing a robust distinction between spin-conserving helical and spin-flip helical (trivial) EM transport. These results establish colored $\Delta_T$ noise as a robust, experimentally accessible, complementary probe for identifying chiral, spin-conserving helical, and spin-flip helical (trivial) EM transport in mesoscopic topological systems.

We employ machine learning techniques to estimate the amount of information contained in three Krylov-space observables: the spread complexity $C(t)$, the discrete Wigner negativity $N(t)$, and the normalized negativity $\chi(t)=N(t)/|S(t)|$, where $S(t)$ is the survival amplitude. We study thermofield-double evolutions on GUE, GOE and Poisson spectra, and on the integrable $SL(2,R)$ Krylov chain of a two-dimensional CFT primary, with Lanczos coefficients $b_n=\alpha\sqrt{n(n+2h-1)}$. To introduce chaos we add a GUE random matrix to the integrable chain, $H(\varepsilon)=H_{SL(2,R)}+\varepsilon R_0 W_{GUE}$, where $R_0$ is its spectral half-width. Either $C(t)$ or $N(t)$ alone determines the thermofield temperature, with $R^2\simeq0.999$. However, neither can reconstruct the fine structure of the spectral form factor. In the integrable sector all three observables carry the same information. When we turn on chaos an asymmetry appears: $\chi$ predicts $C$ better than $C$ predicts $\chi$. This gap grows from $+0.33$ to $+0.77$, while the same gap for the raw negativity decays to zero. The extra information comes from the survival amplitude, and $\chi(t)$ carries it while $C(t)$ can still be recovered from $\chi(t)$. We derive a lower bound on this gap, set by the fraction of the variance of $\chi$ that comes from $S$.

The QCD axion with charm-only Peccei-Quinn coupling evades the isospin-violation problem of light-quark models in $\chi$PT. Since $m_c>\Lambda_{\rm QCD}$, we employ heavy meson chiral perturbation theory (HMChPT) to constrain this GeV-scale axion, including its CP-even radial partner $\sigma$ and the axion $a$. In HMChPT, $\sigma$ enters at leading order with $O(1)$ coupling, while $a$ couples only at $O(1/m_c)$ and manifests via axion-pion mixing with $\theta_{a\pi}\simeq f_\pi/f_a\sim0.04$. We analyze $D$-meson masses, $D$-$D^*$ splitting, charmonium, $D$-$D$ scattering, $B_s$ mixing, rare $D$ decays, and the channels $K^+\to\pi^+a$, $B\to K a$. No fatal HMChPT constraint emerges, unlike the $\chi$PT isospin issue. The strongest bound is from $\sigma$-mediated $B_s$-$\bar B_s$ mixing; axion-pion mixing opens testable rare decays, though rates are slightly below current sensitivity.

We investigate a generalized Friedberg–Lee (FL) framework for neutrino masses, focusing on the singular parameter space at Point D ($\alpha = \beta = -1/3$). At this limit, the neutrino mass matrix exhibits a democratic texture governed by the $S_3$ permutation symmetry. Although theoretically profound, the exact democratic limit is phenomenologically excluded as it predicts a degenerate mass spectrum and a vanishing reactor angle ($\theta_{13}=0$). To reconcile this high-symmetry limit with experimental observations, we introduce a minimal and systematic perturbation that preserves the Twisted Friedberg–Lee (TFL) symmetry. This mechanism effectively lifts the mass degeneracy and breaks the magic and $\mu$–$\tau$ symmetries in a controlled manner. Our derivation avoids ad hoc parameters, establishing a robust framework that yields a realistic inverted mass hierarchy ($m_3=0$), a non-zero $\theta_{13}$, and intrinsic CP violation. We demonstrate that the model predicts maximal atmospheric mixing and a significant Dirac CP phase. The obtained numerical ranges for the neutrino masses and the Jarlskog invariant show excellent agreement with global fit data, providing a theoretically motivated foundation for neutrino flavor physics within the TFL scheme.

We consider the non-Abelian bosonized Thirring model for a semi-simple group $G$ at level $k$, with deformation parameter $\lambda$. We compute the two-point correlation functions of current and composite current operators to cubic order in $\lambda$, assuming large values of the quadratic Casimir $c_G$ of the group $G$ in the adjoint representation. From these, we extract the $\beta$-function and the anomalous dimensions of both the current and composite current operators, showing the absence of an additional critical point of order $k/c_G$. Our findings align with those of Destri & de Vega for the Fermionic non-Abelian Thirring model, but contradict the claim in Dashen & Frishman regarding the existence of an additional fixed point of order $1/c_G$.

The symmetry properties of the phase diagram of dense quark matter composed of $u$ and $d$ quarks with three colors have been investigated in the framework of massless (3+1)-dimensional Nambu–Jona-Lasinio (NJL) and QCD models. It turns out that in the presence of baryon $\mu_B$, isospin $\mu_I$, chiral $\mu_5$ and chiral isospin $\mu_{I5}$ chemical potentials, the Lagrangians of these models are invariant under the so-called dual transformation ${\cal D}$. In this paper, it has been shown that the path integration measure of the corresponding partition functions is also invariant under ${\cal D}$. Consequently, the entire NJL model (or QCD) thermodynamic potentials are dually symmetric. In particular, it means that in the total $(\mu_B,\mu_I,\mu_5,\mu_{I5})$-phase portraits of these models the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugate (or symmetrically) to each other. Dual symmetry between CSB and charged PC phases of quark matter is a fundamental property of massless dense QCD; it should be observed in the framework of any approximation to the QCD phase diagram, and have important implications for studies of the phase structure.

We show that scalar discrete-series unitary irreducible representations (UIRs) $\Pi_{p,0}$ ($p=1,2,\cdots$) of the de Sitter (dS) group $\mathrm{SO}_0(1,4)$ admit a dS-covariant Krein realization on the dS hyperboloid, endowed with a dS-invariant non-degenerate Klein-Gordon (KG) sesquilinear form, in which the group action is indecomposable and organizes naturally into a Gupta-Bleuler triplet. The positive- and negative-norm sectors are already present in the underlying Krein space, whereas a null sector emerges only at an intermediate stage, where the induced KG form becomes degenerate and its radical leads canonically to the physical quotient carrying the UIR $\Pi_{p,0}$. We further show that suitable limits of the bulk theory at the “future” and “past” conformal boundaries ${\mathcal{I}}^\pm$ give rise to dS-invariant boundary realizations endowed with induced kernel inner products. While the bulk negative-norm sector admits no independent boundary counterpart, the boundary realization retains the physical and gauge structures inherited from the bulk. The resulting boundary module nevertheless remains indecomposable, with its physical quotient carrying the discrete-series representation $\Pi_{p,0}$. The antipodal symmetry provides a natural relation between the realizations on ${\mathcal{I}}^+$ and ${\mathcal{I}}^-$, ensuring the consistency of the boundary construction and its geometric interpretation. At the heart of the analysis lies a Fourier-type bulk-boundary transform that provides a dS-covariant identification of the bulk and boundary physical sectors, establishing a one-to-one intertwining correspondence between the bulk and boundary realizations of $\Pi_{p,0}$ while preserving reflection positivity.

This chapter is intended as an introduction to dense matter and the equation of state of neutron stars and their mergers. It begins with a brief description of neutron star interiors, followed by a historical overview of the theoretical frameworks used to describe them focusing on relativistic formalisms, including different degrees of freedom, models, symmetries, and phases. It also provides an overview of our current understanding of dense matter (including theory, experiments, and observations) and discusses the advances we expect to see in the field over the next decade.

We consider a self interacting charged scalar field represented by the complex {\lambda}{\phi}4 model, embedded in a background electric field exhibiting classical stochastic fluctuations. We studied the effects of the classical stochastic noise on the physical parameters of the scalar field theory, for both weak and ultra strong electric field regimes. The stochastic background electric field is included in the Schwinger propagator through the covariant derivative, and the generating functional of the theory is found by means of the replica trick in order to compute the statistical average over electric fluctuations. As a result of the averaging process, an effective interaction between charged currents emerges, with a coupling constant proportional to the magnitude of the auto-correlation function of the electric field fluctuations. We obtained the dressed propagators, the interaction vertices, and the renormalization group equations of the theory, along with the corresponding streamplots in the manifold of interaction couplings.

We investigate gravitational lensing in Kerr spacetime in the presence of a modified photon propagation law arising from higher-curvature effective field theory corrections. Adopting a deformed dispersion relation, we analytically derive the deflection angle and the propagation time delay for null trajectories in a rotating background. We show that the modified propagation leads to explicit and calculable deviations from the standard Kerr predictions, affecting both the bending angle and the time delay. These corrections exhibit a nontrivial dependence on the black hole spin and are expected to become more relevant in the strong-field regime. In particular, near the photon region-where the spin-dependent geometry influences photon trajectories-such effects may play a role in shaping observable propagation features. Our results establish a concrete and systematic framework to quantify deviations from standard photon propagation in gravitational lensing. They further indicate that observables such as relativistic image separations and time delays provide a potential avenue to probe ultraviolet corrections to gravity in strong-field environments.

We present a comprehensive study of the current-phase relation of the Josephson junction in a holographic superfluid ring, realized from the stochastic and non-equilibrium dynamics according to the Kibble-Zurek mechanism. By employing a spatially modulated charge density to engineer a weak link, the current-phase relation is investigated in a range of geometric and thermodynamic parameters. The seminal sinusoidal relation between the current and the phase emerges periodically due to the compact shape of the geometry. We also identify the relations between the critical current and the geometric parameters of the junction: the width, steepness and depth. Furthermore, we demonstrate that the critical current exhibits a characteristic exponential decaying against the final temperature, reflecting the thermal degradation of the order parameter in a strong-coupling regime. Our results establish a robust framework for holographic Josephson devices, offering experimentally testable predictions for the non-equilibrium dynamics of high-$T_c$ superconductors.

We investigate the matrix model of two-color two-flavor QCD (matrix-QCD$_{2,2}$) in regimes with large baryon ($\mu_{_B}$), isospin ($\mu_{_I}$), and/or chiral ($c$) chemical potentials. In these regimes, the Hamiltonian simplifies considerably, making it possible to investigate the ground state for intermediate and strong Yang-Mills coupling. By diagonalizing the Hamiltonian using the variational techniques, we show that in regimes where $\mu_{_B}$ and $c$ (or $\mu_{_B}$ and $\mu_{_I}$) dominate, tuning the remaining parameters leads to quantum phase transitions (QPTs). These transitions form a complex web of phases, each of which has a ground state uniquely labelled by baryon number $B$ and isospin $I$. Several of these phases are LOFF-like, characterized by a ground state carrying non-zero spin and hence spontaneously breaking rotational symmetry. These results are consistent with older effective field theory predictions by Splittorff-Son-Stephanov \cite{Splittorff:2000mm}. The fermionic content of these LOFF-like ground states consists of spin-1 di-(anti-) quarks which are analogous to Cooper pairs. We compute the spin-fraction carried by the quarks and find that it constitutes a significant portion – in some cases nearly the entirety – of the total spin.

Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen–Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard $U(1)$ symmetry-resolved reflected entropy in a thermal $U(1)_k$ CFT is equipartitioned at leading order, excluding a universal $\log|n|$ term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe $U(1)_k$ Chern–Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number $\nu$, its normalised phase is $2\pi\kappa pn\nu/k$, where $\kappa\in\mathbb Z$ is the mixed topological coupling; for $\gcd(\kappa\nu,k)=1$, a discrete Fourier transform reconstructs $n\bmod k$. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale $\ell_\star r_+/L^2=1.128378\ldots$ determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.

Non-Lorentzian theories of gravity, most common of which are Galilean and Carrollian gravity, arise from General relativity under suitable scalings. General relativity can be obtained by gauging the Poincaré algebra. A convenient formulation of non-Lorentzian gravity follows the contraction of the Poincaré algebra in the tangent space to its non-Lorentzian counterparts, e.g. Galilean and Carrollian algebras. In existing literature, different non-Lorentzian theories of gravity have been addressed separately. In this paper, we introduce a single unified framework of expansion to address all these different theories. We show that different scalings can be unified into a single covariant form parametrized by $(s,n)$, alongside the contraction parameter $\epsilon$. Keeping these parameters unfixed in the limit $\epsilon \to 0$ defines a $\textit{unified flat geometry}$ and its $\textit{unified algebra}$, which reduces to a specific non-Lorentzian geometry for a particular choice of $s$ and $n$. Using this setup in the tangent space, we systematically expand the Einstein-Hilbert action in even powers of $\epsilon$, which we call a $\textit{unified expansion}$ of Einstein's gravity, whose leading-order theory is fixed by $(s,n)$. This reproduces various classes of gravitational theories, including Einstein gravity (the trivial case), Galilean gravity, Carroll gravity, all of which can be extracted from this expansion. Using the expansion, we then formulate String Carroll (SC) gravity, where the local metric has two vanishing eigenvalues. The near-horizon region of generic non-extremal black holes has been recently shown to be a SC geometry. By considering explicit examples, we confirm that these near-horizon geometries constitute solutions of SC gravity, paving the way of understanding physics near the horizon of generic black holes in terms of SC gravity.

A diagonal light-front overlap contains near-forward energy-momentum-tensor (EMT) information but is not itself a local matrix element. In the large-$N_c$ 't Hooft model we complete the second GPD moment with its ERBL contribution and follow how the two support regions combine. Boundary exponents generate fractional powers and, at $\beta=1/2$, resonant logarithms in the separate terms. We show that these structures cancel, including the interference of the leading and next indicial families. At the resonance, cancellation of the double and single logarithms also yields an inverse-mass-squared residue sum rule; above it, the two regions combine into a finite fourth-order coefficient. The complete EMT form factor is therefore analytic through curvature order. The ERBL sector leaves the slope unchanged but is essential for curvature and higher derivatives. We extract stable canonical and heavy curvatures, estimates with systematic envelopes for the second and third light excitations, and the longitudinal trace radius. The intermediate-state decomposition further shows how constituent mass and excitation redistribute pole strength and generate removable poles and interference zeros.

We derive a novel recursive structure for dimensionally regularised scalar one-loop Feynman integrals based on Schläfli's differential formula for hyperbolic simplices. The recursion relates the Laurent coefficients in the dimensional regulator $\varepsilon$ of an $N$-point integral to lower-order coefficients of integrals with additional external legs. The construction is seeded by the $\varepsilon=0$ contributions, which admit a geometric interpretation as volumes of simplices in hyperbolic space and are known in terms of multiple polylogarithms (MPLs). Iterating the recursion therefore provides a constructive algorithm for computing arbitrary orders in the $\varepsilon$-expansion of scalar one-loop integrals with arbitrary masses and kinematics, while remaining entirely within the class of MPLs. In particular, this establishes that all coefficients in the Laurent expansion of dimensionally regularised scalar one-loop integrals can be expressed in terms of MPLs. As a first application beyond existing results, we obtain an explicit closed MPL expression for the $\mathcal{O}(\varepsilon)$ coefficient of the scalar hexagon with arbitrary masses and off-shell Euclidean kinematics.

We construct an $R^2$ cosmology based on scale invariance and unimodular gravity in which the Goldstone boson of dilatations establishes a predictive connection between inflation and dark energy. The conservation of the corresponding Noether current confines the inflationary trajectory to a one-dimensional orbit in field space, freezing the Goldstone direction and rendering the inflationary dynamics effectively single field. After inflation, the system settles on a Minkowski vacuum manifold. The unimodular integration constant, already present in the full theory but negligible during inflation, lifts the flat Goldstone direction, generating an exponential potential for the canonically normalised field. Unlike in phenomenological quintessence models, its slope is not a free DE parameter, but is instead fixed by the field-space geometry inherited from the inflationary attractor. This geometry excludes matter-era tracking and, throughout the inflationary viability region, places the field in the thawing regime compatible with accelerated expansion. For a representative inflationary benchmark, the now pseudo-Goldstone field remains frozen until close to the present epoch, yielding DE equation-of-state parameters $(w_0,w_a)\simeq(-0.992,-0.011)$ in the CPL parametrisation $w(a)=w_0+w_a(1-a)$. More generally, the same parameter controlling the inflationary spectral tilt also fixes the slope of the DE potential, leading to a tight correlation between early- and late-Universe observables: increasing the thawing signal lowers $n_s$, while values of $n_s$ closer to unity drive the model towards $\Lambda$CDM.