This work introduces a field-theoretical model designed to simulate the presence of material layers with magnetoelectric properties. The model comprises the standard Maxwell field coupled to a Chern-Simons field confined to a planar layer. The electromagnetic behavior of the boundary is emulated through the interaction between the Chern-Simons and Maxwell fields, governed by two parameters: the Chern-Simons mass and the coupling constant between the fields. Both parameters can be adjusted to reflect the specific properties of different materials. We compute the exact propagator of the theory and employ it to investigate several physical properties. Our analysis focuses on phenomena that arise from the presence of external sources coupled to both the Maxwell and Chern-Simons fields, considering various scenarios. In the Chern-Simons sector, the sources emulate defects in the crystal lattice of the material layer. The main objective of this paper is to present the proposed model and to explore its behavior in the simple context of a single planar material interface. We also suggest possible extensions of the model to more general configurations.

Brazil

F.A. Barone

H.L. Oliveira

J.P. Ferreira

Two-gauge field model for magnetoelectric boundaries

We investigate second-order gravitational perturbations in asymptotically AdS black branes, developing a gauge-invariant framework to compute the amplitude ratio between quadratic and linear quasi-normal modes. Our analysis reveals resonant divergences of this ratio when the summed frequencies of two source modes coincide with the frequency of a third mode. These divergences are shown to manifest as poles in three-point fully retarded correlators of the energy-momentum tensor in the holographically dual quantum field theory, establishing a concrete connection between bulk gravitational nonlinearities and observables in the dual boundary theory. Our findings contribute to the understanding of nonlinearity in quantum many-body systems while deepening the holographic dictionary between spacetime dynamics and quantum correlations.

China

Wen-Bin Pan

Zhangping Yu

Yi Ling

The second-order quasi-normal modes for AdS black branes

We show that the Standard Model Yukawa matrices satisfy a set of simple yet nontrivial inequalities. The relations we derive are independent of the basis used to define the fermion fields, and, amongst other things, place strong constraints on the alignment of the columns of the up-type and down-type Yukawa matrices, as well as their cofactor matrices. The reason why one can obtain such strong statements can be traced back to the hierarchical nature of the fermion masses and quark mixings. The inequalities should be seen as very strong necessary conditions on the SM Yukawa couplings and thus are useful for constraining flavor models.

Gero Gersdorff

Lucas Modesto

Inequalities for Standard Model Yukawa couplings

Multi-particle correlations between azimuthal angle and mean transverse momentum are a powerful tool for probing size and shape correlations in the initial conditions of ultra-relativistic nuclear collisions. These correlations have also been employed to investigate the structure of the colliding nuclei, including potential nuclear shape phase transitions at the energy frontier. However, the direct implementation of these correlations is highly nontrivial, and prior studies have been mostly limited to lower-order correlations, such as the modified Pearson correlation coefficient, $$\rho (v_\textrm{n}^{2}, [p_\textrm{T}])$$ . This paper presents a unified framework that employs a recursive algorithm, enabling the efficient evaluation of arbitrary-order correlations while maintaining computational efficiency. This framework is demonstrated using widely adopted transport models, including AMPT and HIJING. The proposed unified algorithm for multi-particle correlations between azimuthal angle and transverse momentum provides a systematic and efficient approach for multi-particle correlation analyses. Its application in experiments at the Relativistic Heavy Ion Collider and the Large Hadron Collider facilitates the exploration of nuclear structure at ultra-relativistic energies.

Denmark

Emil Nielsen

Nina Nathanson

Kristjan Gulbrandsen

You Zhou

A unified algorithm for multi-particle correlations between azimuthal angle and transverse momentum in ultra-relativistic nuclear collisions

We numerically evaluate, for slab entangling geometries, the mutual information and the holographic entanglement entropy between strongly interacting fields in different spatial regions for two different conformal holographic models at finite temperature and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-charge density. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mrow><mi>R</mi></mrow></mrow></math>-Charge Black Hole (1RCBH) model describes a strongly interacting fluid with a critical point in its phase diagram, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mrow><mi>R</mi></mrow></mrow></math>-Charge Black Hole model has no critical point. In both models, we find that the mutual information tends to be overall reduced by increasing the value of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>/</mo><mi>T</mi></math> at larger values of the separation length <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> between two disjoint spatial regions of the medium, while the opposite tendency is observed at lower values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. We also observe that, very close to the critical point of the 1RCBH model, the mutual information tends to increase with increasing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>/</mo><mi>T</mi></math> in the stable branch of black hole solutions. Moreover, the mutual information between the fields in the two disjoint regions is observed to be enhanced by increasing the characteristic size <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> of these regions, with such an enhancement asymptotically saturating, thus suggesting the existence of a finite field correlation length between the disjoint regions of the system. The finite part of the entanglement entropy may change sign depending on the values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mo>/</mo><mi>T</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math>, and it correctly detects the critical point of the 1RCBH model, a feature that is also adequately detected by the mutual information.

Gustavo de Oliveira

Ronaldo F. Costa

Lucas C. Céleri

Romulo Rougemont

Mutual information and holographic entanglement entropy for strongly coupled <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi></mrow></math>-charged plasmas

Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, <a href="http://dx.doi.org/10.1103/pcvc-734h">Phys. Rev. Lett. 134, 241901 (2025)</a>.] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.

United States

Daniel C. Hackett

Michael L. Wagman

Lanczos algorithm for lattice QCD matrix elements

We propose a physical scheme of a uniformly accelerated Unruh–DeWitt battery and utilize quantum work extraction as a probe to witness the thermal nature of the Unruh effect induced by the accelerated motion. By employing the open quantum system approach, we analyze the coherent and incoherent components of the ergotropy which is the maximum amount of quantum work extraction of the relativistic battery driven by a coherent field. It has been proved that the steady values of coherent quantum work extraction in the asymptotic condition is only determined by the acceleration-dependent Unruh temperature. The asymptotic behavior of coherent ergotropy can demonstrate the thermal nature of the Unruh effect with respect to the Kubo–Martin–Schwinger condition. Under the circumstance of the Unruh effect, we explore the effect of the phase of the coherent charging field on the dynamics of coherent ergotropy when the battery approaches to the same thermal equilibrium state. The variation in the phase of the coherent driving field can improve the energy storage capacity of a relativistic battery. From viewpoint of energy transfer, the relativistic battery is helpful to examine the Unruh thermality.

Canada

Wei-Wei Zhang

Tian-Xi Ren

Yin-Zhong Wu

Xiang Hao

Coherent quantum work extraction of a relativistic battery as a probe for acceleration-induced Unruh thermality

We present here the first lattice simulation of symplectic quantization, a new functional approach to quantum field theory which allows to define an algorithm to numerically sample the quantum fluctuations of fields directly in Minkowski space-time, at variance with all other present approaches. Symplectic quantization is characterized by a Hamiltonian deterministic dynamics evolving with respect to an additional time parameter $\textit{τ}$ analogous to the fictious time of Parisi-Wu stochastic quantization. The difference between stochastic quantization and the present approach is that the former is well defined only for Euclidean field theories, while the latter allows to sample the causal structure of space-time. In this work we present the numerical study of a real scalar field theory on a 1+1 space-time lattice with a $\textit{λϕ}$ interaction. We find that for $\textit{λ}$ ≪ 1 the two-point correlation function obtained numerically reproduces qualitatively well the shape of the free Feynman propagator. Within symplectic quantization the expectation values over quantum fluctuations are computed as dynamical averages along the dynamics in $\textit{τ}$, in force of a natural ergodic hypothesis connecting Hamiltonian dynamics with a generalized microcanonical ensemble. Analytically, we prove that this $\textit{microcanonical}$ ensemble, in the continuum limit, is equivalent to a $\textit{canonical-like}$ one where the probability density of field configurations is $\textit{P}$ [$\textit{ϕ}$] ∝ exp($\textit{zS}$[$\textit{ϕ}$]/ℏ). The results from our simulations correspond to the value $\textit{z}$ = 1 of the parameter in the canonical weight, which in this case is a well-defined probability density for field configurations in causal space-time, provided that a lower bounded interaction potential is considered. The form proposed for $\textit{P}$ [$\textit{ϕ}$] suggests that our theory can be connected to ordinary quantum field theory by analytic continuation in the complex-$\textit{z}$ plane.

Italy

Martina Giachello

Francesco Scardino

Giacomo Gradenigo

Symplectic quantization: numerical results for the Feynman propagator on a 1+1 lattice and the theoretical relation with quantum field theory

The Weak Gravity Conjecture imposes stringent constraints on effective field theories to allow for an ultraviolet completion within quantum gravity. While substantial evidence supports the conjecture across broad classes of string theory-derived effective field theories, constructing low-dimensional models realizing it explicitly remains highly non-trivial. In this work, we illustrate how the presence of multiple gauge fields in an effective field theory significantly complicates the bottom-up implementation of the Weak Gravity Conjecture. To this end, we introduce a general algorithm that constructs the convex hull associated with a given set of superextremal states and verifies whether it satisfies the Convex Hull version of the Weak Gravity Conjecture. We show that the computational time of this construction grows exponentially with the number of gauge fields, thereby revealing a fundamental obstruction to concrete, algorithmic realizations of the conjecture in theories with many gauge fields.

Germany

Stefano Lanza

The computational complexity of the Weak Gravity Conjecture

String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as $$ {e}^{\ell^2\square /2} $$ in the vertices. This nonlocality has hindered the development of a consistent Hamiltonian formalism, leading some to question whether such a formalism is even viable. To address this challenge, we introduce a toy model inspired by string field theory and construct its Hamiltonian formalism by demanding that it reproduce all correlation functions derived from the path-integral formalism. Within this framework, we demonstrate for this toy model that physical-state constraints can be imposed to eliminate negative-norm states, while zero-norm states decouple from the physical state space. This approach provides a novel perspective on the nonlocality inherent in string field theories.