Papers

We study positivity properties of exact observables in planar N=4 super Yang-Mills as functions of the 't Hooft coupling. Motivated by analogous results in quantum mechanics, we ask whether such observables admit a once-subtracted dispersion representation in the coupling over a positive spectral measure. Our main result is that this property, also known as the Stieltjes property, holds for a broad class of exact observables. We prove it analytically, through integral representations, for the octagon anomalous dimension, the logarithm of the circular Wilson loop, the Bremsstrahlung function, and anomalous dimensions in the BMN limit, and we provide numerical evidence for the cusp and tilted cusp anomalous dimensions. We also identify quantities for which the Stieltjes property does not hold, and study the weaker positivity property of complete monotonicity. The Stieltjes property yields two powerful consequences: it lets us turn perturbative input into rigorous non-perturbative bounds, and bootstrap perturbative coefficients. We also show how the strong-coupling expansion and its non-perturbative corrections can be recovered from the once-subtracted dispersion representation via a Mellin-Barnes representation and outline a method to estimate the strong-coupling expansion from weak-coupling data.

Recent works have pointed out the existence of a holographic constraint on (extremal) three-point functions of scalar moduli in scale-separated AdS vacua. Moreover, it has been shown that this constraint is satisfied in the DGKT scenario in massive type IIA for the original $\mathbb{T}^6/(\mathbb{Z}_3 \times \mathbb{Z}_3)$ orbifold, as a result of a series of unexpected cancellations. We extend the analysis to more elaborate scenarios, involving geometries with less symmetry and more complicated triple-intersection numbers. Surprisingly, the cancellations persist in all examples with $h^{2,1}=0$, leading us to speculate this conclusion might hold more generally.

We investigate the supercritical thermodynamics of Euler-Heisenberg AdS black holes within the framework of Lee-Yang phase transition theory. We show that the system admits two distinct critical points associated with a four-phase thermodynamic structure and identify a degenerate higher-order critical point where the two criticalities merge. Extending the thermodynamic description into the complex domain, we determine the distribution of Lee-Yang singularities and construct the corresponding complex phase diagrams. At the degenerate critical point, we find that a well-defined Widom line emerges despite the absence of a conventional coexistence curve, acting as an effective stability boundary in the supercritical regime. In the two-critical-point regime, the complex phase diagram exhibits two distinct Widom lines, one associated with a coexistence curve and the other arising solely from the complex singularity structure. We further show that the Lee-Yang formalism consistently reproduces the expected phase structure for systems with a single critical point and in the absence of criticality. Our results reveal a rich supercritical phase structure and provide new insights into the origin and physical interpretation of Widom lines.

Quantum fields exhibit a rich entanglement structure which is still not fully understood. In this work, we study the entanglement structure of the vacuum state of a massless scalar field in (1+1)-dimensions – a paradigmatic case for both high energy and condensed matter physics. We fully characterize the entanglement negativity between two arbitrary compact spacelike-separated regions of the field by calculating the logarithmic negativity along with the modes carrying it, called negativity cores. We achieve this using a framework based on the Kähler structure of Gaussian states, wherein we calculate the diagonalization of the operator associated with the partially-transposed restricted linear complex structure. In doing so, we extend the methods of this framework by proposing a basis-independent definition of the transpose operation. The explicit diagonalization we perform is enabled by a reformulation of the eigenvalue problem as a boundary value problem in the complex plane. Our results also suggest extensions to higher dimensions and fermionic fields.

Symmetries plays a significant role in understanding the conservation laws in Quantum field theories. Here, we attempted a quadratic type dimensionless gauge transformation to achieve the invariance in QFTs. We have shown the extensive study of invariance of complex scalar, Abelian and Non- Abelian theories and established the conservation laws. We included an explicit graphical analysis to invoke the invariance. This is studied in a physical context, where different field configurations correspond to the same physical state. The necessity of the covariant derivative is studied in detail, highlighting how it ensures consistent transformation under local symmetry operations. The meaning of covariance is clarified as the preservation of the form of physical laws under transformations.

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

We study the late-time relaxation of a neutral relativistic viscous fluid in $d+1$ dimensions. In the long-wavelength regime, linearized hydrodynamics predicts that the sound mode at momentum $nk$ decays as $e^{-n^2\omega_I t}$. However, nonlinear analysis gives a decay of $e^{-n\omega_I t}$. We derive a closed asymptotic attractor solution in which the frequency of the $n$-th harmonic locks to $n$ times the complex frequency of the fundamental mode. The amplitude envelopes for energy current $J$ obey a simple cascading relation, $J_n=\alpha_J^{\,n-1}J_1^n$, with $\alpha_J$ fixed by the equation of state, the longitudinal viscosity, and the fundamental wavenumber. For conformal fluids, $\alpha_J=1/(8\eta k)$, in agreement with the holographic result of arXiv:2512.07242. The existence of the attractor shows that, even near equilibrium, field powers are not equivalent to amplitude order.

The recently introduced formalism of chiral cluster seeds replaces quantum cluster variables with deformed vertex operators. In this framework, a decorated quiver associated with a seed encodes the operator product expansions of the corresponding vertex operators. This formalism is applied to several $(q,t)$-deformed W-algebras, including $\mathcal{W}_{\mathfrak{q},\mathfrak{t}}(\mathfrak{gl}(N|M))$, $U_q(\widehat{\mathfrak{sl}}_2)$, and the deformed Bershadsky–Polyakov algebra. In particular, it is shown that different free field realizations of the currents are related by mutations of the associated chiral cluster seed. The second part of the paper introduces a $(q,t)$-deformation of the subregular W-algebras, denoted by $\mathcal{W}_{\mathfrak{q},\mathfrak{t}}^{\text{sub}}(\mathfrak{sl}(N))$. All free field realizations obtainable through seed mutations are described. An embedding of $\mathcal{W}_{\mathfrak{q},\mathfrak{t}}^{\text{sub}}(\mathfrak{sl}(N))$ into the free field realization of $\mathcal{W}_{\mathfrak{q},\mathfrak{t}}(\mathfrak{sl}(N))$ tensored with a rank-two Heisenberg algebra is constructed. This embedding may be viewed as a deformed analogue of inverse quantum Hamiltonian reduction. The relation between the subregular algebras and $\mathcal{W}_{\mathfrak{q},\mathfrak{t}}(\mathfrak{gl}(1|N))$ is also discussed.

Using the soft-gluon theorem, we identify a soft-recoil mechanism by which unresolved gluon radiation induces decoherence in the spin correlations of heavy quark-antiquark pairs produced by longitudinally polarized virtual photons in deep-inelastic scattering. Upon tracing over the unresolved gluon, the reduced spin density matrix is block diagonal in the mirror parity of the production plane and is governed by two coefficients: a parity-odd normal-spin flip, which reduces the normal-axis correlation, and a parity-even stochastic rotation of the spin-correlation plane about its normal, which suppresses the in-plane spin coherences while leaving the normal-axis correlation unchanged. From the complete tree-level next-to-soft amplitude with the exact color-octet structure we derive both coefficients, together with the trace and antisymmetric in-plane terms, in closed form. The parity-odd coefficient is the larger one, by a factor of at least $3.5$, and grows as the inverse square of the heavy-quark transverse momentum. We estimate the resulting reduction of concurrence and Bell-CHSH violation, and propose an infrared-safe, radiation-binned EIC observable, formed at fixed Born kinematics after longitudinal-transverse separation, which isolates the two channels. We estimate its size, including multiple wide-angle emissions in an independent-emission model, the conditions under which detector and kinematic effects cancel, and the statistics required. The latter, however, exceed the yield of exclusive heavy-baryon pairs at nominal EIC luminosity by several orders of magnitude, makes the observable elusive for the measurement accessible in that channel.

Gauge theories of massive $p$-forms are connected by various dualities, which hold classically but may be broken at the quantum level. One example is the $BF$ theory of topologically coupled $p$- and $(d-p-1)$-forms in $d$ dimensions, where the coupling between forms results in a manifestly gauge invariant mass term for either form when the other is integrated out classically. We perform the path integral quantisation of this theory; by integrating out one of the forms, the resulting determinants are sensitive to the topology of spacetime, and counterterms must be introduced to renormalise their divergences. We compute these determinants in terms of the topological numbers of spacetime, showing explicitly how the quantum duality of the massive theories is broken on topologically non-trivial backgrounds. This is directly related to the quantum breaking of the massless duality between the form that was integrated out and the longitudinal modes of its partner. In particular, the difference of counterterms is proportional to the Euler characteristic of spacetime. The existence of gravitational instantons suggests that these dualities may be broken even in Minkowski space in the presence of topological fluctuations.

The Weak Gravity Conjecture (WGC) is a swampland criterion of long standing: any consistent theory of quantum gravity must contain a charged particle whose charge-to-mass ratio exceeds that of an extremal black hole, so that gravity remains the weakest force. The AdS/CFT correspondence offers a calculable boundary handle on bulk gravity, and the imaginary parts of bulk quasinormal modes are read off the boundary as poles of a retarded Green's function. We show that the WGC follows from this boundary calculation in two settings that fall outside the Reissner–Nordström idealisation: static spherically symmetric black holes in dRGT massive gravity, and dyonic black holes in Einstein–ModMax non-linear electrodynamics. The chain runs from the metric and gauge field, through the charged Klein–Gordon equation, into a near-horizon scaling limit whose radial equation reduces to Whittaker form; the conformal weight $\nu_0$ then enters a damping-time inequality. For the dRGT black hole every massive-gravity parameter ($\alpha,\beta,m_g,h$) cancels out, leaving the universal saturation $q/(m r_+) \geq 1/\sqrt{2} \approx 0.707$. For the Einstein–ModMax black hole the duality-symmetric non-linearity parameter $\gamma$ survives, and yields $q/(m r_+) \geq e^{-\gamma/2}$, which reduces to the Reissner–Nordström bound $q/(m r_+) \geq 1$ in the Maxwell limit $\gamma \to 0$. Either result is of order unity, and the second weakens monotonically as the non-linearity grows. We then relax three of the simplifying assumptions of the dRGT derivation, namely exact extremality, minimal coupling, and the absence of higher-curvature terms. The cancellation breaks. Each correction reintroduces $m_g,\alpha,\beta$ into the bound through a controlled functional dependence, and we tabulate and plot the relaxed forms across parameter space.

This paper presents the first non-perturbative lattice determination of the Yang–Mills topological susceptibility slope $\chi^\prime$ in the large-$N$ limit. This quantity represents the $\mathcal{O}(p^2)$ term of the momentum expansion of the topological charge density two-point correlator, and has important theoretical and phenomenological implications for strong interactions. This calculation is based on a novel algorithm that avoids topological freezing at large $N$ on fine lattices, and on a novel method to reliably compute $\chi^\prime$ on the lattice. The results of this study are relevant for the description of the proton spin in deep inelastic scattering experiments via the Shore–Veneziano formula.

We consider a black hole solution embedded in a mass varying dark matter (DM) halo and study scalarization induced by DM. We derive the required conditions on the scalar DM coupling that allow for a regular bound state scalar cloud. We find that such configurations exist only for quantized coupling values in terms of the halo's intrinsic parameters (for Hernquist, this reduces to the inverse of the compactness). This study provides a novel connection between DM phenomenology and scalarization around a black hole.

The discard ZX-calculus, a diagrammatic language for mixed-state quantum mechanics, is used to give a nonperturbative, categorical proof of the Bloch-Nordsieck cancellation of infrared divergences in QED. Soft photons are treated as an open quantum system: the resolved charged particles and hard photons form the system, while photons below a detector resolution form the environment. The reduced hard channel is a completely positive trace-preserving (CPTP) map, and the soft-photon theorem replaces the full S-matrix by a controlled displacement operator whose Feynman-Vernon influence functional satisfies the equal-history normalization ${\cal F}[J,J]=1 $. In the ZX-calculus, this normalization is a single diagrammatic identity: the doubled displacement diagram collapses to the bare wire under the unitarity, cyclicity, and discard rules. The proof therefore serves as a categorical consistency check on the open-system treatment of soft QED given in a companion paper; it confirms that the physical derivation is logically complete and free of hidden assumptions about the infrared limit. For off-diagonal hard-state elements, the same diagram yields the coherent-state overlap, giving a first-principles account of soft-cloud decoherence. The soft-shell coarse graining is then constructed as a CPTP Schur channel whose infinitesimal limit produces the exact Lindblad generator with jump operators determined by the eikonal emission amplitudes. Finally, a local CPTP-certification pipeline is developed for non-Markovian process tensors, enabling constant-time verification of trace preservation in open quantum simulations. The framework bridges categorical quantum semantics, non-equilibrium field theory, and practical open-system compilation.

This study formulates observer-dependent Krylov spreading for non-inertial quantum systems driven by linear Bogoliubov transformations. Starting with the closed single Rindler-pair $SU(1,1)$ sector, we show that its Lanczos basis is identical to the Rindler pair-number basis. As a result, the Krylov spread complexity reduces exactly to the mean number of correlated Rindler pairs, $C_k=\vert\beta_k\vert^2$. Within this framework, we demonstrate that Krylov spreading dynamics are governed by the competition between the detuning parameter and the coupling constant, naturally dividing the dynamics into three distinct regimes. Notably, Krylov complexity becomes localized in the detuning-dominated regime. By extending this to a multimode, strictly quadratic Bogoliubov Hamiltonian, we find that inequivalent Rindler wave-packet pairs violate the $C_k=\vert\beta_k\vert^2$ correspondence, thereby highlighting the single-pair $SU(1,1)$ model as an exactly solvable, observer-adapted benchmark. In such multimode scenarios, the mean pair-number eigenstates no longer dictate Krylov complexity. Overall, our work provides a new perspective for analyzing Krylov complexity in non-inertial quantum systems.

We examine the size effects in the Sommerfeld enhancement factor for puffy dark matter annihilation. First, we use the partial-wave method to study the case of puffy dark matter for which only a charge density distribution is given without specifying its internal structure. We find that by using two dimensionless parameters, we can provide a characterization of the resonance structure of the Sommerfeld enhancement. Using this approach, we demonstrate that the finite size of dark matter particle is another fundamental factor, in addition to low velocity, that affects the Sommerfeld enhancement. Then, as an example of puffy dark matter with nontrivial internal structures, we perform the analysis for the nugget-type dark matter, whose Sommerfeld enhancement factor is found to exhibit a resonant behavior similar to that of point-like particles.

We present a formulation for color confinement on the basis of quantum reference frames (QRFs) and relational observables. In the QRF approach to color confinement, colored quantities are not defined as isolated local fields, but rather as relational observables with respect to a color frame or a dressing field. The Gauss law removes compactly supported local color charge from the physical bulk algebra, while boundary fluxes, Wilson lines, and holonomies may remain as semi-local data. This separates gauge invariance from frame independence. Color confinement is characterized under the fixed protocol by the absence of a finite-energy, physically accessible, asymptotically isolated nontrivial color-charged representation in the infinite volume limit. A failure to globalize a long-distance color frame is one possible mechanism contributing to this absence, which clarifies the role played by topological defects in color confinement. As concrete examples, we examine $(1+1)$-dimensional $SU(2)$ Yang–Mills theory and $(1+1)$-dimensional $U(1)$ gauge–Higgs model. We also take up the two-dimensional U(1) gauge–Higgs model on $\mathbb{H}^2$ (Euclidean $AdS_2$) and three-dimensional $SU(2)$ gauge–Higgs model on $\mathbb{H}^3$ (Euclidean $AdS_3$) which are obtained based on conformal equivalence by dimensional reduction of four-dimensional SU(2) Yang–Mills theory restricted to symmetric-instanton sectors. Through explicit calculations in these examples and in controlled sectors, we provide nontrivial checks for internal consistency of the present formulation. We also discuss prospects for four-dimensional Yang–Mills theory and gauge–Higgs theories.

Naturalness is commonly presented as an objective constraint on physical theories: a model requiring fine-tuning is judged implausible. This presentation conflates a representation-dependent quantity with an invariant one. A fine-tuning verdict depends on the choice of fundamental parameters, the prior, and the measure convention, so it does not by itself fix a feature of the world. Here, I argue that what is objective is structural: the universality class of the map from parameters to observables, invariant under admissible changes of parametrization and measure convention, and independent of any prior over parameter space; it constitutes an informational invariant. On this account naturalness is neither an aesthetic preference nor an objective probability, but a statement about the distinguishability geometry of the representations through which physics encodes observation. I trace the certainty of naturalness verdicts to a tradition, from Ockham through Dirac and Weinberg, in which parsimony and beauty are taken as guides to truth; modern naturalness inherits that tradition's authority without its successive justifications. The argument is developed in the gravitational and cosmological sector, where naturalness reasoning is sharpest and its effective-field-theory grounding is weakest. A uniform analysis across gravitational and particle dark matter candidates shows that fine-tuning tracks the analytic structure of the abundance map, not the nature of the candidate; that the resulting classification is invariant across measure conventions while the tuning number is not; and that this decomposition instantiates informational structural realism. I situate the position against the autonomy-of-scales account, which the argument largely accepts, and against the deflationary reading, which identifies the borrowed authority but discards the structural residue.

We derive parity-even transverse-traceless metric-like cubic vertices for massless bosonic higher-spin fields in AdS$_3$. Starting from the known two- and three-derivative vertices in three-dimensional flat space, we construct their AdS$_3$ extensions by imposing gauge invariance and accounting for dimension-dependent identities. The result is shown to be consistent with minimal coupling to gravity.

We present a new method together with a proof-of-concept implementation for determining the Landau singularities of Feynman integrals, read off directly from where the Euler characteristic of the associated integral drops. Working over finite fields makes the requisite elimination tractable for multi-scale integrals at the multi-loop frontier. The algorithm returns the genuine and complete set of singularities, subject to a set of conditions which are practically testable. We apply these methods to classes of Feynman integrals beyond the reach of current methods, including non-planar six-point diagrams at two loops, as well as a fully massive three-loop envelope graph. Several of the newly found singularities, both in $d$- and 4-dimensional external kinematics, are of unexpected complexity when compared to previously known singularities for these examples.

Given a local gauge theory on spacetime with boundary, it naturally defines another gauge theory which can be regarded as a theory of the boundary values. For Lagrangian theories, it comes equipped with the presymplectic structure which can be used to define one or another version of Hamiltonian-like formulation of the initial model. This relation is especially manifest for AKSZ sigma models and more-generally gauge PDEs with compatible presymplectic structure in which case the boundary system is again a gauge PDE with presymplectic structure. In the context of (flat space) holography one is interested in boundaries at infinity, also known as asymptotic boundaries. The gauge PDE framework naturally extends to this setup, resulting in the notion of gauge PDE with asymptotic boundaries. Although this works perfectly well at the level of equations of motion, the extension to Lagrangian systems appears quite subtle because the presymplectic structure capturing the Lagrangian is divergent at the boundary. We show that any $Q$-cocycle in the bulk (and presymplectic structure in particular) determines a pair of compatible $Q$-cocycles of the boundary gauge PDE: the renormalized one of the same ghost-degree, and the anomaly cocycle of degree one lower. For the latter, the construction is somewhat analogous to the residue map known in the context of b-geometry. The general formalism is exemplified by scalar and Maxwell fields on AdS and Minkowski spaces. It turns out that in the AdS case the natural action determined by the anomaly presymplectic structure is precisely the one known as the holographic Weyl anomaly in the AdS/CFT context while its null-infinity counterpart was known in a few very particular cases only.

Recently, the NNLO perturbative QCD pressure of cold and dense symmetric matter, with arbitrary quark masses, has been resummed within the renormalization-group-optimized perturbation theory (RGOPT) framework. By being imbued with renormalization group properties, the resulting pressure is less sensitive to renormalization scale ($\Lambda\equiv X \mu_B/3$) variations than the NNLO perturbative QCD pressure. Here, we extend this by considering $\beta$-equilibrium and charge neutrality to evaluate the corresponding equation of state (EoS). We provide a compact “pocket" fitting formula for the EoS for $N_f=2+1$ massive quarks at different renormalization scale parameter ($X$) values. We describe pure quark stars as well as hybrid stars with quark-cores. Pure quark stars compatible with astrophysical observations were obtained with $X=2.71-3.30$, whereas a larger value (3.84) is needed if the secondary component of the observation GW190814 represents a neutron star. Hybrid stars were built considering three representative hadron models based on a relativistic mean-field description, and chosen to produce soft and stiff EoSs. Stable hybrid stars with masses compatible with the massive pulsar PSR J0740+6620 were obtained considering $X$ of the order of 2 to $2.71$, the largest scale giving rise to hybrid stars with a large quark core with a radius of 2 to 8 km , and the smallest to a small quark core at the center of the star.

We have studied holographic entanglement entropy in a moving thermal gauge theory with a non-zero chemical potential. A sufficiently high velocity enhances the holographic entanglement entropy, particularly for larger values of the chemical potential. However, at high temperature and velocity, the chemical potential dependence is almost entirely washed out, indicating that thermal fluctuations dominate over charge-density effects. In the ultrarelativistic regime, the holographic entanglement entropy grows very rapidly with velocity, which emerges as the dominant parameter, largely suppressing both thermal and chemical contributions.

We discuss the algebraic structure of observables in Schrödinger CFTs. These operators have zero mass (or particle number) and generically transform in staggered ”pyramid representations” built from ”alien operators,” as we explain with the doubled state-operator correspondence. We comment on implications for the space of non-relativistic CFTs, thermal physics, and generalize the exceptional symmetry conservation laws of Bekaert, Meunier, and Moroz, and Golkar and Son. We show that alien operators are analogous to double-twist operators in Lorentzian CFT, with systematic cross-channel corrections from massless particles when they exist.

Precise derivation of the logarithmically scale-dependent Hamiltonian eigenstate picture for hadrons in the space of virtual quark and gluon states of the canonical front form of QCD requires addressing first the problem of divergences stronger than logarithmic, and especially the small-x divergences in the dynamics of gluons. We propose to facilitate the regularization and cancellation of these divergences using a gluon mass parameter and an auxiliary color-octet scalar field corresponding to the longitudinally polarized gluons. The auxiliary field decouples from the hadronic constituent dynamics when the mass parameter tends to zero, as required in the gauge theory. The same method applies in the cancellation of the quadratic ultraviolet transverse divergences in the self-interactions. After explaining how the method works in computations of the scattering amplitudes, we describe its application to the bound-state eigenvalue problems. We focus on the results it leads to already in the second-order weak-coupling expansion for effective Hamiltonians of heavy quarks. They include the concept of confinement in an effective theory with the gluon mass parameter sent to zero and a heuristic scenario concerning extension of the Hamiltonian approach to the dynamics of light quarks.

We derive a new beta-type basic hypergeometric integral identity from the equality of supersymmetric partition functions on $\mathbb{RP}^{2}\times\mathbb{S}^{1}$. Unlike previously known identities obtained from lens-space partition functions, this integral does not appear to arise as a degeneration of the lens elliptic beta integral. Our result enriches the collection of basic hypergeometric beta integrals arising from supersymmetric dualities and has applications to supersymmetric gauge theories, integrable models, and the theory of special functions.

The nature of the $G(3900)$ structure, observed in $e^{+}e^{-}\to D\bar{D}$, remains unclear and may stem either from a genuine resonance or from charmonium interference and threshold effects. We therefore propose searching for the $G(3900)$ signal in the reaction $K^- p \to D_s^- \Lambda_c^+ G(3900)^0$, where the interference effects present in $e^{+}e^{-}\to \bar{D}^{*}D$ are absent. We employ an effective Lagrangian approach, where the reaction proceeds via a central production mechanism dominated by $t$-channel $D^{0}$ and $D^{*0}$ exchanges, based on the possible interpretation of $G(3900)$ as a $P$-wave $\bar{D}^{*}D$ molecular state, whose coupling to the $\bar{D}^{*}D$ channel is fixed from our previous fit to the $e^{+}e^{-}\to \bar{D}^{*}D$ data. The $\bar{K}N$ initial-state interaction, mediated by Pomeron and Reggeon exchanges, is also included and leads to a significant enhancement of the production cross section. If measured in future experiments, the predicted total cross sections and angular distributions can provide a promising probe of the nature of the $G(3900)$, and in particular of its possible genuine resonance nature.

We study the dynamics of a Hamiltonian system with a ghost degree of freedom, characterized by a negative kinetic-energy contribution and the possibility of runaway behavior due to an indefinite energy functional. We present numerical evidence that a nonlinear interaction term, together with a saturating exponential potential $V_c$, can suppress phase-space escape over the parameter ranges explored in this work. Using direct numerical integration of the Hamiltonian equations of motion, Poincaré surfaces of section, and trajectory projections, we find that the ghost sector and nonlinear couplings generate a mixed phase-space structure with both regular islands and chaotic regions. The maximal Lyapunov exponent supports bounded chaotic motion: nearby trajectories separate exponentially while remaining confined to a finite region of phase space for the investigated initial conditions and parameters $(\varepsilon,\alpha)$. These results suggest that nonlinear confinement can significantly alter the stability properties of negative-energy sectors at the classical level. They provide numerical evidence for a bounded-chaos regime in which ghost-induced divergences are avoided within the explored domain.

The Sugawara construction provides a natural way to construct the Virasoro algebra from a current algebra. It was shown in Ref.~\cite{Ghazi:2025oin} that for the $u(1)^2$ Kac-Moody current algebra, there exist additional constructions that exhibit a $\mathbb{Z}_N$-graded structure. Indeed, the space of such constructions defines a non-compact algebraic variety whose dimension depends on $N$. In this paper, we consider the compactification of these algebraic varieties by adding points at infinity to the non-compact part, and show that these points correspond precisely to generalizations of $BMS_3$-like algebras. More explicitly, for a $\mathbb{Z}_2$ grading, the corresponding algebra coincides with the $BMS_3$ algebra, which takes the form $\mathrm{Vir} \rtimes F$, where $F$ is an infinite abelian ideal of the full algebra. For $N > 2$, we show that there exist generalizations of the standard $BMS_3$ algebra of the form $\mathrm{Vir} \rtimes F$, where $F$ is a nonabelian ideal that forms a nilpotent algebra of depth $r < N$. We further demonstrate that the depth of the algebra is related to the order of the singularity of the algebraic variety at that point. We also show that the polynomials defining the algebraic varieties exhibit a factorization property into linear factors, which, if true, classifies all $BMS_3$-like algebras. Finally, we study the central extensions of these algebras, which are consistent with the general structure of algebras corresponding to primary fields of conformal weight $h = 2$.

We provide a field-theoretic construction of Padmanabhan's duality-invariant Feynman propagator for a massive point particle in Euclidean space $\mathbb{R}^D$. Padmanabhan's propagator includes quantum-gravity effects due to the existence of a quantum of length $\ell$. Including $O(\ell^2)$ corrections, the corresponding field-theory model turns out to be a free, massive scalar defined in $\mathbb{R}^{D+2}$. The two additional dimensions with respect to the original $\mathbb{R}^D$ provide the necessary room, so to speak, for quantum-gravity fluctuations.