Papers

Many-body topology is a central concept in modern theories of solids, and identifying effective degrees of freedom that capture it is important both fundamentally and practically. This work studies the extent to which geometric information of an interacting many-body ground state can be inferred from a finite number of local correlations. Starting from the Resta formula, $ z=\left\langle \exp\!\left(\frac{2\pi i}{L}\hat X\right)\right\rangle$, we view $\log z$ as the cumulant generating function and establish a generic information hierarchy across cumulant orders. We show that, for an $N$-particle system, even complete knowledge of all density correlators up to order $N-1$ does not, in general, uniquely determine the Berry phase $\gamma=\operatorname{Im}\log z \, (\mathrm{mod}\ 2\pi)$. In the thermodynamic limit, the statement becomes stronger: no finite set of local correlators suffices to determine the global holonomy. We also identify two exceptional yes-go cases in which the hierarchy is broken. First, for quasi-free models, all cumulants are determined by the particle two-point correlation function. Second, symmetry-enforced constraints can reduce the infinite cumulant sum entering $\log z$ to finite information. The argument is analytic and does not rely on a specific microscopic Hamiltonian. Our results clarify a limitation of approaches based on local degrees of freedom for many-body holonomy and provide a minimal framework for distinguishing when global holonomies are encoded in local correlations and when they are not. We also comment on the possibility of analogous hierarchies in other contexts, such as the quantum marginal problem in quantum information theory and many-body scattering problems. Finally, we discuss implications for future numerical work, including machine-learning approaches to the search for topological phases.

Recent time-domain analyses suggest that black hole stability may be sensitive to localized near-horizon geometric deformations, while the underlying spectral mechanism remain unclear. In this work, after verifying the instability of the model in the time domain, we systematically investigate quasi-normal mode spectra under static localized non-positive perturbations within a frequency-domain framework. We find that such deformations generically induce a new purely imaginary mode. As the deformation approaches the horizon, the imaginary part of this mode increases and eventually enters the upper half complex-frequency plane, signaling the onset of black hole instability. Numerical results reveal clear scaling relations between the critical distance for instability and the deformation strength. We further derive rigorous proofs for our discoveries in frequency domain. These results demonstrate that black hole stability under long scale is conditionally sensitive to localized deformation of metric near the horizon and establish a unified spectral framework for understanding their induced instabilities.

Primordial black holes (PBHs) are black holes generated in the early universe without having gone through stellar evolution. In the standard formation process, PBHs are formed from super-horizon primordial fluctuations with non-linearly large initial amplitude. In order to simulate the non-linear gravitational dynamics of PBH formation, one has to rely on numerical relativity solvers to approximate the solution of the Einstein equations. COSMOS is a C++ package for solving the Einstein equations in 3+1 dimensions, providing simple tools for the simulation of PBH formation. In order to resolve the collapsing region, non-Cartesian scale-up coordinates and a fixed mesh-refinement procedure are implemented. In COSMOS, a massless scalar field and a perfect fluid with a linear equation of state are implemented as matter fields. To achieve a practically acceptable computational speed, OpenMP is used for the parallelization. COSMOS has no other dependencies, which makes for an easier installation.

Oscillating spacetime curvature can drive particle production during reheating, whose accurate modeling requires the use of non-perturbative out-of-equilibrium methods. Tachyonic instabilities have previously been studied using 2-Particle Irreducible (2PI) formalism in the Hartree approximation, which however misses important momentum exchanging interactions. We present a self-consistent approximation scheme for reducing the non-local next-to-leading order 2PI equations of motion to local quantum kinetic equations, which can be solved with standard methods. We pay special attention to interactions involving unstable modes during tachyonic instabilities.

We study semidefinite programming (SDP) methods to analyze spin chain Hamiltonians. We examine the ground state energy, the first excited charged states and ground state correlators in two simple models: the Ising model in a transverse magnetic field and the closely related 3-state Potts model. Our goal is to understand precisely what the SDP program is doing and when it works well, why it does so. We focus on the following novel ingredients: using charge constraints to obtain excited states and to see if additional constraints from integrable models are effective at improving the method. At criticality we also explore to what extent we can use approximate Virasoro correlators to extract conformal data: the central charge and some critical exponents of charged states. We also use these to identify the location of the phase transition. In the special case where the system is made of free fermions we prove that the SDP finds the exact energy of the ground state and produces the correct two point functions of the fermions. Away from free fermion theories, the SDP gets progressively worse at estimating data beyond the value of the ground state energy (like correlation functions), although it qualitatively matches these. In order to be effective, the SDP seems to run into scaling issues where the amount of input needed scales poorly with the lattice volume.

We found sets of exact analytic quasi-stationary states of a massive scalar field in a dyonic Kerr-Sen black hole~(DKSBH) background in the maximally extended spacetime region. A central novelty is the use of horizon-regular ingoing Eddington-Finkelstein coordinates, which enables a direct and unambiguous imposition of the ingoing boundary condition at the horizon. The exact radial solutions are in the form of confluent Heun functions. Imposing regularity at spatial infinity enforces a series truncation condition, yielding an exact quantization of the quasi-stationary frequencies. The spectrum exhibits a rich multi-branch structure, which we show splits into two distinct classes: modes that are insensitive to the black hole spin and charges and modes that explicitly depend on them. We uncover a clear asymmetry between co-rotating and counter-rotating configurations, driven by the spin-angular momentum coupling, as well as a systematic shift of the spectrum induced by electric and magnetic charges. The physical branches exhibit a universal behavior: modes with positive real frequency possess positive imaginary parts and therefore grow exponentially in time, whereas modes with negative real frequency are damped and decay. This suggests that positive-energy excitations in the region behind the outer horizon including the inner region of the inner horizon which contains the closed-timelike-curve, exponentially destabilize the background spacetime, supporting Hawking's chronology protection conjecture. In addition, the purely imaginary modes contain no oscillatory component and hence do not propagate through the spacetime, preventing traveling excitations along closed timelike curves and remaining consistent with the conjecture.

By studying a simple model of relativistic particles propagating through a background medium with an energy-dependent relaxation time that is unbounded from above, we investigate how long-term memory obstructs the emergence of local hydrodynamics in systems with a gapless non-hydrodynamic sector. In the RTA matching frame, we show that the full gradient expansion is generically divergent in most flows, even for Fourier modes, and that any resummation necessarily retains an infinite set of slow non-hydrodynamic degrees of freedom. The divergence of the gradient expansion therefore reflects a more fundamental breakdown of hydrodynamic locality caused by persistent non-hydrodynamic memory. We finally show that sufficiently singular relaxation spectra can invalidate ordinary diffusion itself. In these regimes, the diffusivity diverges, and the late-time dynamics become superdiffusive, governed by intrinsically nonlocal constitutive relations.

In connection with the question of confinement of massive ghost in quadratic gravity (QG), color confinement in quantum chromodynamics (QCD) has been reconsidered in the superfield formalism. It is shown that when a bound state in the BRST transformation of the gluon field exists, the gluon becomes massive and is confined. It is also shown that the asymptotic field of the gluon field obeys the field equation for not the conventional massive Klein-Gordon field but the massive dipole field. In case of quark confinement, it is shown that the quark field satisfies the massive spinor dipole equation in the confinement phase, which might suggest a physical picture such that a pair of quark and anti-quark constitutes a bound state and is confined into a meson. These facts encourage us to conjecture that the similar phenomenon could take place in confinement of massive ghost, which violates the unitarity of the physical S-matrix, and might provide us with a resolution to the unitarity problem in QG.

We investigate the observational differences between the Ellis–Bronnikov (EB) wormhole and the Schwarzschild black hole (BH) by performing general relativistic radiative transfer (GRRT) simulations. We consider a spherically symmetric steady-state accretion flow and perform GRRT simulations incorporating synchrotron emission. For both the EB wormhole and the Schwarzschild BH, the simulated images consist of a central shadow region and a bright photon ring. We find that both the shadow region and the photon ring of the EB wormhole are brighter than those of the Schwarzschild BH. These differences arise from the absence of an event horizon in the EB wormhole, allowing the emission from the accreting matter around and beyond the throat to contribute to the observed intensity. We also compare the simulated images with the Event Horizon Telescope (EHT) observations of M87* and find that both the EB wormhole and the Schwarzschild BH are in reasonable agreement with the current EHT results.

It is a difficult task to detect the indivisible quanta of weakly interacting radiation fields, and even more challenging to probe their quantum statistics. Nevertheless, if barely functional high-quality resonant detectors are feasible for weakly interacting radiation fields, they do come with certain statistical advantages to probe quantum effects at the seemingly classical limit of a large number of quanta of the incoming radiation field. We present correlated counting, homodyne, and heterodyne detection strategies using high-quality resonant quantum harmonic detectors operating at this limit, initialized in bolometry-inspired zero-mean preparations such as thermal states. We compare the bolometric regime of good resonant harmonic detectors in quantum optics to the bolometric regime of barely functional resonant mass quadrupole oscillators as detectors for quantum gravity. Simple statistical tests are proposed using symmetric correlators for two and three such barely functional resonant mass detectors that could reveal the complementary quantum noise characteristics of gravitons in tabletop experiments.

We present quantum-mechanical calculations of bremsstrahlung in the $^{124}$Sn + $^{124}$Sn at 25 MeV/u reproducing the measured photon spectrum over the full energy range. For the first time, we quantitatively determine the incoherent-to-coherent ratio in the photon spectrum. This ratio is extremely small, ranging from $10^{-11}$ to $10^{-4}$, which demonstrates that coherent emission dominates throughout the measured energy range. This behavior is in sharp contrast to proton-nucleus scattering, where incoherent emission dominates because of the leading role of nucleon magnetic moments. This contrast is illustrated by the TAPS Collaboration data for $p + ^{197}{\rm Au}$ collisions at a proton beam energy of 190 MeV, where the corresponding ratio reaches $10^{3}$-$10^{5}$. We find that incoherent-to-coherent ratios explain the difference between the two spectra in unified picture: (1) In proton–nucleus scattering, the spectrum contains a pronounced hump, (2) In $^{124}$Sn + $^{124}$Sn scattering, the spectrum decreases monotonically and has a nearly logarithmic shape. Our results identify a previously unexplored quantum regime of bremsstrahlung emission in nuclear reactions and open a new route for studying coherent effects in heavy-ion collisions.

We develop a holographic framework for continuous higher-form symmetries and their low-energy effective descriptions, based on bulk path integrals, holographic renormalisation and boundary-condition-changing deformations. We show how approximate higher-form symmetries associated with a defect current can be realised holographically through massive antisymmetric tensor fields, either via parametrically small bulk masses or strong deformations associated with Robin boundary conditions. We further study the consequences of massless and massive Hodge dualities in the bulk, deriving the corresponding dualities between boundary theories related by different quantisation choices. Our results provide a unified perspective on approximate symmetries, dualities and strong/weak-coupling relations in holographic theories based on massive $p$-forms. In the self-dual case of an exact symmetry of degree $(d-3)/2$, we derive generalised constraints on holographic current-current correlators in the presence of double-trace deformations.

We study the pseudo-gauge transformation (PGT) freedom at freeze-out in relativistic spin hydrodynamics. The Cooper–Frye map is shown to factor through the quotient of freeze-out data by a universal stabilizer, yielding a stratified fibration over the space of thermodynamic Lagrange multipliers. This classifies observables into base and fiber types, bounds the number of independent PGT-sensitive observables by the family-restricted fiber dimension, and implies cross-observable consistency relations. Applied to heavy-ion polarization data, the fibration structure provides a structural interpretation of the tension between $\Lambda$ polarization and $\phi$-meson spin alignment as evidence that the vorticity-dominated response sector may need to be enlarged with local field-correlation data. We show that Weyl-anomaly-induced currents studied recently are classified as base observables and recover the known Belinfante–canonical obstruction $\Omega_{ab}\neq\varpi_{ab}$ from the stabilizer condition.

We extend previous studies on a novel class of unstable two-level systems which were called Critical Unstable Qubits (CUQs). In an appropriately defined co-decaying frame, the CUQs exhibit striking phenomena of indefinite anharmonic oscillations between two states and coherence-decoherence oscillations of mixed states. These features are distinct from the usual Rabi oscillations observed in the Hermitian counterpart of two-level systems, which are harmonic and preserve the coherence of the quantum state. We employ the density matrix formalism to study these phenomena for mixed states and delve into the nature of the trajectory traversed by these states in the Bloch sphere by studying the time evolution of the Bloch vector that describes the quantum state of the unstable qubit. In particular, we provide for the first time explicit geometric constructions to obtain trajectories of both pure and mixed CUQs in and on the Bloch sphere. This enables us to identify the stationary points of CUQs, at which the states do not evolve in time in the co-decaying frame. The potential implications of our findings for particle cosmology and quantum simulations of non-Hermitian Hamiltonians are discussed.

In this paper, we provide a short review on the Quintom dark energy theory. Firstly, we discuss the No-Go theorem associated with dynamical dark energy, then present some examples of models in which the equation of state (EoS) evolves with time and can cross $w=-1$ . Secondly, we discuss the bouncing universe and emergent universe with Quintom matter. Finally, we discuss the possibility of studying the nature of dark energy by measuring the Cosmic Microwave Background (CMB) polarization rotation angle.

We develop the Boltzmann-Wasserstein (BW) distance, a temperature-dependent metric on the space of quantum theories, defined as the optimal $W_2$ distance between Boltzmann-weighted energy spectra. Computing it is an optimisation over wormholes: each unitary identification of the two energy bases defines a coupling of the two boundaries in the doubled Hilbert space, and the optimum - the comonotone partition function $C_{\max}$, which pairs states by rank - is the dominant wormhole connecting the two theories. For semiclassical theories differing by a small entropy shift, the normalised BW distance collapses to a squared horizon-area comparator, $\tilde{\mathcal{W}}^2 \approx (\delta A/4G)^2/8$, with the two areas evaluated at equal energy. When the Hamiltonians differ by an operator $V$, the BW distance equals a long-time average of the real-time thermal two-point function of $V$; when the thermal one-point function of $V$ vanishes - for instance for $V$ odd under an unbroken discrete global symmetry - a four-point representation appears at the next order. On the gravity side we construct the classical saddle that computes $C_{\max}$: a Schwinger-Keldysh wormhole built from two Euclidean caps sharing a single horizon, joined by Lorentzian segments that adiabatically interpolate between the two theories. Its on-shell action reproduces the spectral saddle of $C_{\max}$ - both the saddle-point conditions and the on-shell value - and the Lorentzian segments are essential: a purely Euclidean interpolation is exponentially suppressed. The saddle captures only the rearrangement of the spectrum; the perturbative representations retain in addition the variance of the matrix elements of $V$, invisible to the classical geometry. We work out two examples - two BTZ black holes with different cosmological constants and a $T\bar{T}$ deformation of BTZ.

We provide a systematic framework for computing the logarithmically divergent part of one-loop partition functions on product spaces $\mathrm{AdS}_{d_A} \times S^{d_S}$ of arbitrary dimension. By expanding the higher-dimensional kinetic operators in spherical harmonics, we reduce the ($d_A+d_S$)-dimensional spectral problem to an infinite tower of $d_A$-dimensional determinants, which are then represented via spectral $\zeta$-function methods. We isolate the logarithmic divergences arising from the interplay between the individual AdS determinants and the infinite Kaluza-Klein sum, carefully accounting for the contributions of zero modes on the sphere that produce additional AdS determinants. We test this framework on different fields and apply it to the complete multiplet of 11-dimensional supergravity on $\mathrm{AdS}_4 \times S^7$. We recover in a 4d language the result of arXiv:1210.6057, namely that the only non-vanishing logarithmic divergence originates entirely from the 2-form AdS mode in the ghost sector, reproducing the well-known $\frac{1}{4}\log N$ correction to the ABJM free energy predicted by supersymmetric localization.

Traversable wormholes are among the most interesting solutions of gravitational theories, but within General Relativity they generally require exotic matter violating the null energy condition. Modified gravity theories with matter-geometry coupling provide a promising framework in which wormhole geometries may instead be supported by effective gravitational contributions. Motivated by this possibility, we investigate rotating traversable wormholes in $f(R,T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the energy-momentum tensor, within the slow-rotation approximation. We construct stationary and axisymmetric wormhole solutions supported by an anisotropic fluid and show that the obtained geometries are regular, asymptotically flat, horizonless, and satisfy the flare-out condition at the throat. A central result is that the matter sector satisfies both the null and strong energy conditions, indicating that traversable rotating wormholes can be supported without exotic matter. We further analyze particle motion, frame dragging, and non-geodesic effects arising from matter-geometry coupling, together with shadow deformation and gravitational lensing signatures induced by rotation. A preliminary stability analysis based on sound-speed conditions indicates the physical viability of the solutions. These results demonstrate that rotating wormholes in $f(R,T)$ gravity constitute physically consistent compact configurations with potentially observable astrophysical signatures.

The microphysics underlying non-baryonic dark matter remains unknown. I derive the two-species Schrödinger-Poisson-Yukawa system for spin-1/2 dark-sector fermion fields, $\psi$ (mass $m_1$) and $\chi$ (mass $m_2$), coupled through a scalar mediator of mass $m_\phi$ via a universal Yukawa coupling, within an orbital-free density-functional framework with the Kirzhnits gradient coefficient $\lambda_B=1/9$. A central result is that the Bohm potential, far from being negligible in the Thomas-Fermi regime, contributes a species-dependent surface-energy correction analogous to the nuclear liquid-drop model: the heavier fermion species generates an outward quantum-pressure wall whilst the lighter species provides an inward surface tension, with degeneracy pressure furnishing the bulk confinement. In the single-species Schrödinger-Poisson limit the ground state recovers the benchmarked invariants $M_{\mathrm{dim}}\simeq 3.883$ and $x_T\simeq 2.562$, yielding $M R_T\simeq 9.95\,\lambda_B\hbar^2/(G m_1^2)$. For polytropic index $\gamma=5/3$ the mass-radius relation satisfies $R\propto M^{-1/3}$; for $\gamma=4/3$ a limiting mass emerges above which no stable equilibrium exists. Illustrative configurations span $M=10^{-8}$-$5\, M_\odot$, $m_1\sim 10^{-14}$-$10^{-6}\, eV$, and radii from a few~km to $\sim 10^3\, R_\odot$, with gravitational-wave contact frequencies in the Einstein Telescope and LISA bands and microlensing signatures accessible to current surveys. The predictive rigidity of the resulting mass-radius relation, in which the single microphysical parameter $m_1$ determines the equilibrium radius once the total mass is specified, furnishes a reproducible, first-principles reference for constraining the dark-fermion mass in multi-component dark sectors.

We develop a group-theoretic interpretation of the Unruh effect based on affine symmetry on a light ray and relate it to modular theory. For a massless scalar field in two spacetime dimensions inertial and uniformly accelerated observers select two different flows within the same chiral one-particle structure, respectively, null translations and dilations. Minkowski modes are adapted to translations, while Rindler modes are adapted to dilations, with the Mellin transform providing the natural bridge between them. When a Minkowski positive-frequency mode is restricted to a single Rindler wedge, its comparison with Rindler modes is non-unitary within the positive-frequency sector. Modular theory gives the corresponding operator-algebraic interpretation: on the horizon the modular flow of the half-line algebra is implemented by dilations, and the restricted vacuum satisfies the KMS condition. The affine group thus appears as the minimal symmetry structure underlying thermality on the Rindler horizon.

In this work, first we discuss black holes with quantum corrections as an open quantum system and apply Lindblad formalism to explain the “zig-zag" behavior in the Hawking- Page curve and radiation process, specially by considering the effects of exceptional points. Then, we calculate quantum corrections for various parameters of $3d$ Cotler-Jensen theory which is $\text{AdS}_3$ with reparametrized modes. At each step of the calculations, we compare the results with the case of JT. We then calculate quantum-corrected greybody factor for various black hole solutions, and specially for the case of Cotler-Jensen theory. Finally, we study the effects of quantum corrections on Lyapunov exponent, potential, and quantum information structure of black holes.

We discuss the AdS/CFT correspondence from the viewpoint of the gauge-theoretic formulation of gravity, in which gravity is interpreted as a broken phase of conformal gauge symmetry. In the AdS$_2$/CFT$_1$ case, we show that the Schwarzian derivative naturally emerges from the boundary extrinsic curvature of AdS$_2$ geometry. The relation between the bulk Liouville geometry and the boundary projective structure is clarified. We further discuss the distinction between the bulk conformal gauge algebra with vanishing central extension and the emergent boundary Virasoro structure with nonvanishing central charge. We then investigate the possible structure of the AdS$_4$/CFT$_3$ correspondence, which is directly related to the original four-dimensional formulation of gravity as a broken phase of conformal gauge symmetry. In this framework, the Einstein–Hilbert action with cosmological constant emerges together with a total derivative term. We argue that this structure induces the boundary gravitational Chern–Simons term, whose variation leads naturally to the Cotton tensor. The Cotton tensor is interpreted as the fundamental conformal invariant associated with the residual boundary conformal geometry, playing a role analogous to that of the Schwarzian derivative in AdS$_2$/CFT$_1$. We also discuss the qualitative difference between AdS$_4$/CFT$_3$ and AdS$_5$/CFT$_4$. While the former appears naturally connected with gravity arising from conformal symmetry breaking, the latter may require genuinely higher-dimensional, string-inspired structures beyond the four-dimensional conformal gauge framework. These observations suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken conformal gauge symmetry.

Hawking's original derivation of particle creation by black holes in Schwarzschild spacetime exploits, among various concepts, the exponential dependence on the retarded time variable u of the affine parameter \lambda of the null geodesics that are integral curves of the null vector field orthogonal to the Killing horizon. This exponential law implies that the Schwarzian derivative of \lambda with respect to u is minus a half the square of surface gravity. The black hole Killing horizon inherits an intrinsic projective structure, and the squared surface gravity is the invariant characterizing such a structure. There is therefore evidence that the Bekenstein-Hawking temperature is completely determined from the projective structure on the Killing horizon. As a further test, it is here shown that, in a spacetime model with variable mass parameter, the logarithmic derivative of surface gravity is determined by the Schwarzian of the affine parameter. The Schwarzian in Schwarzschild and Kerr geometries is also studied in detail. All these properties are a first step towards proving that black hole thermodynamics finds its mathematical foundations in the projective geometry of Killing horizons. Such a research program can be applied to the power radiated from a black hole, the rate of change of the black hole mass with respect to the area of the event horizon, the fundamental imaginary frequency of quasinormal modes (and hence the decay rate of black hole perturbations).

A classic theorem of Weyl (1921) states that a Weyl metric – a natural generalisation of a pseudo-Riemannian metric – is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal structure is uniquely determined by its projective structure. We discuss analogous results for suitably defined notions of conformal structure for Galilei and Carroll geometry, i.e. for spacetime geometries arising as the `non-relativistic' and `ultra-relativistic' limits of Lorentzian geometry.

Supersymmetry, originally proposed in high-energy physics, can emerge as a remarkable low-energy structure in condensed matter systems. While emergent supersymmetry at quantum critical points is widely discussed in models with continuous symmetries, real materials are constrained by microscopic discrete symmetries. To address this, we investigate (2+1)-dimensional Gross-Neveu-Yukawa theories coupling Dirac fermions to a complex order parameter with discrete $Z_n$ anisotropy. Using the functional renormalization group, we find that for $n>3$, the anisotropic perturbations are irrelevant at the fixed point, yielding a $\mathcal{N}=2$ Wess-Zumino supersymmetric critical point. In the ordered phase, this dangerously irrelevant anisotropy gives rise to a second characteristic length scale, $\xi'$, alongside the usual correlation length, $\xi$. By tracking mass thresholds along symmetry-broken renormalization group trajectories, we extract the exponents $\nu'$ and $\nu$ without imposing prior scaling assumptions. For the $Z_4$, $Z_5$, and $Z_6$ models, our results support the scaling relation $\nu'/\nu = 1+|y_n|/p$ with $p=2$ in the isotropic framework used here.

We report on recent results concerning neutrino oscillation in the presence of background torsion. In the context of Einstein-Cartan theory, we find new oscillation formulas for constant torsion and linearly time-dependent torsion. The oscillation formulas obtained depend on the orientation of the spin.

We introduce a one-parameter root-$T\bar T$-like flow, $ \partial_\lambda \mathcal{L}=\mathcal{R}_\lambda^{1/\alpha}$, which organizes stress-tensor deformations into irrelevant, marginal, and relevant branches. Within duality-invariant electrodynamics in four dimensions, and equivalently within two-dimensional integrable sigma models, the flow admits a closed-form solution controlled by an auxiliary equation. The marginal point $\alpha=1$ reproduces the root-$T\bar T$ / ModMax branch, while $\alpha<1$ gives irrelevant deformations distinct from the standard Born-Infeld $T\bar T$ flow. For $\alpha>1$, the same construction yields explicit relevant $T\bar T$-like Lagrangians. These results suggest that root-$T\bar T$ flows provide a common organizing principle for duality-invariant and integrable deformations.

Entanglement islands are most easily realized in doubly holographic models with massive gravitons or non-gravitating baths. In wedge holography, however, Neumann boundary conditions on both branes give a normalizable massless graviton, while the island saddle of the purely geometric Ryu–Takayanagi (RT) problem collapses to the horizon. Negative Dvali–Gabadadze–Porrati (DGP) terms can restore nontrivial islands by modifying the endpoint condition, but this branch contains a massive ghost. We propose a different semiclassical mechanism. We keep the wedge gravitational action free of DGP terms and couple the healthy Neumann wedge sector to a unitary defect CFT localized at the codimension-two corner. This sector is distinct from the standard corner CFT dual to the undeformed wedge, so its entropy enters as the ordinary matter-entropy term in the quantum extremal surface (QES) prescription without double counting the wedge RT area. If the defect theory is holographic, this entropy can be evaluated by an auxiliary RT surface. We show that when the wedge endpoint determines the defect entangling region, the auxiliary area can vary in the opposite way to the wedge area while all couplings and central charges remain positive. A local endpoint model gives an isolated stable saddle that dominates over the Hartman–Maldacena (HM) surface at late times. The QES condition then replaces the pure orthogonality condition and permits a non-horizon island saddle in a long-range, massless, ghost-free gravitational theory. Thus, the obstruction to massless islands in minimal wedge holography is not masslessness itself, but the absence of a healthy matter-entropy contribution capable of balancing the horizon-minimizing area variation.

We study the Casimir effect in a class of gauge-invariant nonlinear electrodynamics models designed to admit spontaneously Lorentz-breaking magnetic vacua. The theory is formulated in the Plebański first-order representation, with a single-invariant Hamiltonian potential \(\widehat V(P)\) as the fundamental nonlinear object. In this formulation, nontrivial magnetic vacua are stationary points of the reduced effective Hamiltonian. The symmetry-breaking condition is controlled by \(\Sm(P)\equiv\widehat V_P(P)+2P\widehat V_{PP}(P)\), which also controls the rank of the longitudinal magnetic response and of the Hamiltonian constraint structure. Taking this Lorentz-breaking nonlinear electrodynamics as the model under study, we analyze how the distinction between the regular constant-rank sector and the degenerate magnetic vacuum enters the parallel-plate Casimir spectrum. Linearization around a regular magnetic background \(\bar P\), with \(\Sm(\bar P)\neq0\), yields an ordinary Maxwell-like branch and an extraordinary anisotropic branch controlled by \(\alpha(\bar P)=\widehat V_P(\bar P)/\Sm(\bar P)\). We compute the regularized Casimir energy for magnetic backgrounds perpendicular and parallel to the plates. In the regular-sector limit \(\bar P\to P_\star\), with \(\Sm(P_\star)=0\), the extraordinary branch becomes singular and the parallel-configuration energy diverges. This divergence is not an infinite physical Casimir force; it signals that the regular two-branch optical description cannot be continued uniformly to the rank-changing magnetic vacuum. Direct analysis on the degenerate surface shows that the extraordinary branch does not survive as an independent propagating mode for generic momenta. Thus, quantizing the regular theory and then taking \(\Sm\to0\) is not equivalent to imposing \(\Sm(P_\star)=0\) before quantization.

The causal propagator (or Pauli-Jordan function), which multiplied by $i$ is the spacetime commutator of the field $[\phi(x),\phi(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then present a conjecture for its asymptotic spectral density in a free theory, and give examples that lend evidence to the conjectured scaling. Our work has implications for Lorentzian spectral geometry in much the same way as Weyl's asymptotic law has for Riemannian spectral geometry.