The aim of this study is to examine a non-local short pulse equation and understand how its dynamics differ from those of its classical local counterpart. To achieve this, we introduce a Lax pair and develop a $\textit{k}$-fold Darboux transformation, which forms the analytical foundation for constructing exact solutions. Using this method, we derive various solutions, including breathers and stable and unstable solitons over zero and non-zero backgrounds. The exact solutions are then used to train a neural network-based framework using Levenberg–Marquardt artificial neural networks (LM-ANN), which aims to approximate the solitonic structures. Model performance is evaluated using the relative error norm based on the Euclidean distance between the predicted and exact solutions. Surface plots, contour maps, and error visualizations are presented to illustrate approximation quality. To investigate model sensitivity and robustness, we explore multiple activation functions and network architectures, and introduce Gaussian noise at 1%, 2%, and 3% levels to both training and testing datasets. Monte Carlo simulations with multiple noise realizations are conducted, and statistical performance is summarized using the mean and standard deviation of the relative error. Results are reported through comparative tables and graphical analyses. By integrating analytical soliton construction with LM-ANN-based regression and systematic robustness testing, this study presents a hybrid framework for solving the non-local short pulse equation, offering accurate and stable solutions even under noise, a valuable contribution to the analysis of nonlinear systems affected by uncertainty.

China

H. Riaz

Aamir Farooq

Hybrid analytical and neural-network approaches to the non-local short pulse equation

This paper investigates the dynamical effects of particles moving in the Kerr spacetime and its nine single-parameter modified spacetimes, including Bardeen, Ayon-Beato and Garcia (ABG), Hayward, Kerr–Newman (KN), Kerr–Taub–NUT (KTN), Braneworld Kerr (BK), Kerr-MOG, Kerr–Sen, and Perfect Fluid Dark Matter (PFDM) black holes. Using quasi-periodic oscillation (QPO) observational data, we constrain the free parameters of the ten spacetimes through $$\chi ^2$$ analysis under the relativistic precession model of QPO. We constrain the modification parameters for the nine single-parameter modified spacetimes and provide the spin and mass ranges of three microquasars within the ten spacetime models (including Kerr) at the $$68\%$$ confidence level (CL). The results demonstrate that, at the $$68 \%$$ CL, the QPO data impose stringent constraints on the free parameters, as evidenced by the narrow confidence intervals. Among them, only the KN spacetime yields a modification parameter constraint spanning both negative and positive values (encompassing the Kerr case at zero). In contrast, all other tested geometries mandate positive-definite parameters at $$68 \%$$ CL, demonstrating statistical deviation of the Kerr solution. This highlights the significance of exploring modifications to the Kerr spacetime. Finally, we evaluate the spacetime models using the Bayes factor and the Akaike Information Criterion (AIC). Based on the current QPO observational data, the Bayesian factor analysis indicates that the ABG, Hayward, KN, BK, and Kerr-MOG spacetime have a slight advantage over the Kerr solution, while the Bardeen, KTN, Kerr–Sen, and PFDM spacetime are somewhat inferior to the Kerr model. In contrast, the AIC analysis shows that the Kerr spacetime remains the optimal model under the current QPO data.

Shining Yang

Jianbo Lu

Wenmei Li

Mou Xu

Jingyang Xu

Observational constraints on the Kerr and its several single-parameter modified spacetimes using quasi-periodic oscillation data

The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary operators, as contributions from descendant operators can be resummed into conformal blocks. However, for the MI, the expansion involves primaries from the multi-replica theory, which includes far more operators than those in the original theory. In this work, we develop a method to resum this series, yielding an expansion in terms of the primaries of the original theory, specifically restricted to the two-copy sector. This is achieved by expressing the twist operators in a non-local manner across different replicas and using a modular flow representation to obtain the $\textit{n}$ → 1 limit of the Rényi index. We explicitly compute the resulting “enhanced conformal blocks,” which, surprisingly, provide excellent approximations to the MI of generalized free fields across the full range of cross ratios. Remarkably, this approximation appears to be exact in the limit of large spacetime dimensions.

Netherlands

Cesar Agón

Argentina

Horacio Casini

Umut Gürsoy

Guim Planas

Mutual information from modular flow in CFTs

We explore the non-perturbative aspects of $\textit{c}$ = 1 string with compactified Euclidean time, its 0 + 0 dimensional matrix model duals (at self-dual radius), and 0 + 1 dimensional Matrix Quantum Mechanics (free fermion) description. We calculate the instanton normalizations, disk two-point function, and annulus one-point function in worldsheet formalism using string field theory insights. We further match them with the corresponding predictions from the matrix model descriptions. We also have some results and remarks regarding the multi ZZ instanton normalizations and the general (1, $\textit{n}$) ZZ instanton normalization for $\textit{c}$ = 1 string at both self-dual and generic radius.

India

Rishabh Kaushik

$\textit{c}$ = 1, $\textit{R}$ = 1 and $\textit{N}$ ≫ 1: ZZ instantons in 2D string theory and matrix integrals

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

United States

Erick Arguello Cruz

Grigory Tarnopolsky

Yuan Xin

Precision study of the massive Schwinger model near quantum criticality

This paper presents a novel tagging technique to measure the beauty-quark partial decay-width ratio $$R_b$$ and its forward–backward asymmetry $$A_{\textrm{FB}}^b$$ at the FCC-ee, using $$\mathcal {O}(10^{12})$$ $\textit{Z}$-boson decays. The method is based on the exclusive reconstruction of a selected list of $\textit{b}$-hadron decay modes in $$Z\rightarrow b\bar{b}$$ events at the $\textit{Z}$ pole, which can provide the flavour and possibly the charge of the hemisphere. This approach effectively eliminates the contamination from light-quark physics events and reduces the leading systematic uncertainties arising from background contamination, tagging-efficiency correlations, and gluon-radiation corrections by exploiting the geometric and kinematic properties of beauty hadrons. This results in a total relative uncertainty of the order of 0.01 % for both observables. Furthermore, this precision allows to obtain a commensurate precision on the weak mixing angle $$\sin ^2(\theta _\text {W}^{\text {eff}})$$ compared to the muon forward–backward asymmetry on the order of 0.002 %.

Germany

France

Lars Röhrig

Kevin Kröninger

Romain Madar

Stéphane Monteil

Italy

Fabrizio Palla

Switzerland

Emmanuel Perez

Measuring $$A_\textrm{FB}^b$$ and $$R_b$$ with exclusive $\textit{b}$-hadron decays at the FCC-ee

We revisit dispersive bounds on Wilson coefficients of scalar effective field theories (EFT) coupled to gravity in various spacetime dimensions, by computing the contributions from graviton loops to the corresponding sum rules at low energies. Fixed-momentum-transfer dispersion relations are often ill-behaved due to forward singularities arising from loop-level graviton exchange, making naive positivity bounds derived from them unreliable. Instead, we perform a careful analysis using crossing-symmetric dispersion relations, and compute the one-loop corrections to the bounds on EFT coefficients. We find that including the graviton loops generically allows for negativity of Wilson coefficients by an amount suppressed by powers of Newton’s constant, $\textit{G}$. The exception are the few couplings that dominate over (or are degenerate with) the graviton loops at low energies. In $\textit{D}$ = 4, we observe that assuming that the eikonal formula captures the correct forward behavior of the amplitude at all orders in $\textit{G}$, and for energies of the order of the EFT cutoff, yields bounds free of logarithmic infrared divergences.

Cyuan-Han Chang

Julio Parra-Martinez

Graviton loops and negativity

We study nonperturbative effects of torus partition function of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed 2D conformal field theory (CFT) by resurgence in this Letter and a companion paper. The deformed partition function can be written as an infinite series of the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>. We develop highly efficient methods to compute perturbative coefficients in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> expansion. To exemplify, the first 600 coefficients for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed free boson and free fermion are computed. The method can be generalized to any rational CFTs; we present the key idea in this Letter while relegating details and results to the companion paper. Equipped with the large order perturbative data, we provide convincing numerical evidence that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math> series is asymptotic and not Borel resummable. We extract the nonperturbative contribution by resurgence and propose that they originate from new complex saddle points after analytically continuing the modular parameters in the integral representation of the partition function. The proposal is checked by comparing the predicted asymptotic behavior of the coefficients and large order perturbative data, which match nicely. The implications of these nonperturbative contributions for the Stokes phenomenon, which relates the positive and negative signs of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, as well as possible comparisons with holography, is also discussed.

Jie Gu

Yunfeng Jiang

Huajia Wang

Resurgence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>T</mi><mover accent="true"><mrow><mi>T</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math>-Deformed Partition Function

We compute the four-photon (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math>) operators generated by loops of charged particles of spin 0, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, 1 in the presence of gravity and in any spacetime dimension <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>. To this end, we expand the one-loop effective action via the heat kernel coefficients, which capture both the gravity-induced renormalization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math> operators and the low-energy Einstein-Maxwell effective field theory (EFT) produced by massive charged particles. We set positivity bounds on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math> operators using standard arguments from extremal black holes (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>≥</mo><mn>4</mn></math>) and from infrared (IR) consistency of four-photon scattering (for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>≥</mo><mn>3</mn></math>). We find that both approaches yield nearly equivalent results, even though in the amplitudes we discard the graviton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel pole and use the vanishing of the Gauss-Bonnet term at quadratic order for any <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>. The positivity bounds constrain the charge-to-mass ratio of the heavy particles. If the Planckian <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math> operators are sufficiently small or negative, such bounds produce a version of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>-dimensional weak gravity conjecture (WGC) in most, but not all, dimensions. In the special case of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>6</mn></math>, the gravity-induced beta functions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math> operators from charged particles of any spin are positive, leading to WGC-like bounds with a logarithmic enhancement. In <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><mo>=</mo><mn>9</mn></math>, 10, the WGC fails to guarantee extremal black hole decay in the infrared EFT, thereby requiring the existence of sufficiently large Planckian <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>F</mi><mn>4</mn></msup></math> operators.

Brazil

Pedro Bittar

Sylvain Fichet

Lucas de Souza

Gravity-induced photon interactions and infrared consistency in any dimensions

We elaborate on the resurgence analysis on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed 2D conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>, we develop efficient analytical methods to compute high-order terms of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-series. Based on the asymptotic behavior of the large-order perturbative series, we show that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi></math>-series is asymptotic and extract nonperturbative contributions by resurgence. This paper extends a previous Letter of the same authors to interacting rational CFTs, with Lee-Yang CFT as a concrete example. We also discuss possible implications of the resurgence results on holography.

Resurgent properties of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi><mover accent="true"><mi>T</mi><mo stretchy="false">¯</mo></mover></math>-deformed conformal field theories