We present a comprehensive bottom-up analysis of lepton mass and mixing based on the non-holomorphic $A_{4}$ modular symmetry. Neutrinos are assumed to be Majorana particles, and the light neutrino masses are generated through the Weinberg operator. In this framework, we construct all phenomenologically viable models with minimal number of free parameters, with the Yukawa couplings expressed in terms of polyharmonic Maaß forms of weights $\pm4$ , $\pm2$ , and 0 at level $N=3$ . Without imposing generalized CP (gCP) symmetry, we identify 147 (six) viable models with eight real free parameters that successfully reproduce the current experimental data of the lepton sector for the normal (inverted) mass ordering. When gCP symmetry consistent with $A_{4}$ modular symmetry is included, the number of free parameters is reduced by one, yielding 47 (five) phenomenologically viable models in the normal (inverted) mass ordering. Finally, we present detailed numerical analyses of a representative model for both mass orderings to illustrate these results.

China

Xiang-Yan Gao

Cai-Chang Li

Minimal lepton models with non-holomorphic modular $\textit{A}$ $_{4}$ symmetry * Supported by Natural Science Basic Research Program of Shaanxi (2024JC-YBQN-0004) and the National Natural Science Foundation of China (12547106, 12247103)

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

We derive the asymptotic lattice-spacing dependence $$a^2[2b_0\bar{g}^2(1/a)]^{\hat{\gamma }_i}$$ relevant for spectral quantities of lattice QCD, when using unrooted Staggered quarks. Without taking any effects from matching into account we find $$\min _i\hat{\gamma }_i\approx -0.273, -0.301, -0.913, -2.614$$ for $$N_\textrm{f}=0,4,8,12$$ respectively. Common statements in the literature on the absence of mass-dimension 5 operators from the on-shell basis of the Symanzik Effective Field Theory action are being clarified for a description using strictly local tastes, here playing the role of continuum quark flavours. Potential impact of $$\textrm{O}(a)$$ EOM-vanishing terms beyond spectral quantities is being discussed.

Spain

Nikolai Husung

Logarithmic corrections to O( $$a^2$$ ) effects in lattice QCD with unrooted staggered quarks

We analyze the Starobinsky inflation model and the impact of curvature corrections, particularly a cubic $$R^3$$ term, to assess their behavior in light of the latest observational results from the Atacama Cosmology Telescope (ACT). With the recent sixth data release (DR6), the scalar spectral index was measured to be $$n_s=0.9752 \pm 0.0030$$ , when combined with BAO data from DESI DR2, which appears to exclude the pure Starobinsky model at approximately the $$2\sigma $$ level. In this paper, we implement the Starobinsky inflationary potential directly into the CLASS code, without relying on the slow-roll approximation, and we constrain the number of e-folds of inflation $$N_k$$ using a theoretically motivated range derived from reheating considerations and standard couplings between matter fields and gravity. We show that it is still possible to identify a significant region of parameter space where the Starobinsky model remains highly consistent with the latest observational data. While the pure Starobinsky model remains a compelling candidate for cosmic inflation, we explore how including a cubic $$R^3$$ term can shift its predictions to better align with the Planck and ACT measurements.

Brazil

J. Bezerra-Sobrinho

L. Medeiros

Starobinsky inflation and the latest CMB data: a subtle tension?

A dark-energy-free cosmological model $$(\Omega _{DE} \equiv 0)$$ based on gravitationally induced adiabatic particle creation is proposed. The thermodynamics of particle production yields an effective negative pressure that drives both primordial inflation and late-time cosmic acceleration. The model, characterized by four components and two free parameters $$(\alpha ,$$ $$\beta )$$ , reproduces a $$\Lambda $$ CDM-like expansion for suitable $$\alpha ,$$ while $$\beta $$ introduces small but testable deviations from the cosmic concordance model. Constraints from type Ia Supernovae (Pantheon+SH0ES) and $\textit{H}$($\textit{z}$) data indicate $$\beta \simeq 0.13,$$ suggesting a mild departure from standard cosmology and possible relief of the $$H_0$$ and $$S_8$$ tensions. The resulting classical cosmology evolves smoothly between two extreme de Sitter phases, offering a singularity-free, unified scenario that beyond solving old cosmological puzzles opens a new perspective to handle the tensions plaguing the current cosmic concordance model.

P. Lima

J. Lima

Cosmic expansion driven by gravitational particle production: toward a complete cosmological scenario

We derive model-independent constraints on finite-time inflationary initial states by combining an EFT with physical cutoff $$\Lambda $$ , backreaction control at the initialization time, and a UV–IR reflection principle imposed only on a logarithmic “trans-Planckian band” about the cutoff pivot. For Gaussian, homogeneous and isotropic states, Bogoliubov data $$\beta _k$$ determine the excitation energy density, and backreaction finiteness selects a natural weighted Hilbert norm on this data. We introduce a windowed symmetry defect on the band and an explicit local completion map that enforces the reflection without constraining modes outside the band. Requiring that completion does not move admissible data by an order-one amount in the backreaction norm yields a parametric lower bound on the excitation energy density in terms of cutoff-scale Bogoliubov jets. In the narrow-band regime the defect admits a universal jet expansion, so generic non–Bunch–Davies data require tuned cancellations among cutoff derivatives or a nonzero excitation floor.

United States

Douglas Watson

Italy

Tiziano Valentinuzzi

Stability bounds on inflationary initial states from UV–IR reflection on a trans-Planckian band

In this paper, we update constraints on the Holographic Dark Energy (HDE) model and the Interacting Holographic Dark Energy (IHDE) models in a non-flat universe, building upon our previous work in which the flat HDE and IHDE models were tested using same datasets, including DESI DR2 BAO, the five-year supernovae sample from DES, CMB distance priors, observational Hubble parameter data, and the local measurement of Hubble constant. Our results indicate that in the HDE model, an open universe is supported at $$6\sigma $$ , whereas in the IHDE models a closed universe is favored at over $$3\sigma $$ . The model parameter $\textit{c}$ is anti-correlated with $$H_0$$ in all these models, implying that a resolution to $$H_0$$ tension by reducing the parameter $\textit{c}$ comes at the expense of a Big Rip fate. Furthermore, using AIC, BIC, DIC, and Bayes evidence, we find that within the non-flat framework, the $$\Lambda $$ CDM model remains the most strongly supported by the data, while the HDE model is the most disfavored. Compared with the HDE model, the IHDE models demonstrate markedly improved agreement with the data, and the most strongly supported IHDE model is the one with the interaction term $$Q=3\beta H_{\textrm{0}}\frac{\rho _{\textrm{dm}}\rho _{\textrm{de}}}{\rho _{\textrm{dm}}+\rho _{\textrm{de}}}$$ .

Xiaofang Shen

Bing Xu

Kaituo Zhang

Xiangyun Fu

Qihong Huang

Liangliang Ren

Zelin Zhang

Updated observational constraints on interacting holographic dark energy models in a non-flat universe

In this work, we studied the Ayon-Beato Garcia (ABG) solution describing a nonsingular charged black hole using the moving-puncture method. As the first step, we obtained the BG solution in isotropic coordinates with a new, accurate numerical procedure. By focusing on the situation where there is at least one horizon, where the charge is smaller than or equal to a particular critical value, we show the transition between the wormhole geometry described by the isotropic solution to a time-independent trumpet foliation resulting from the disconnection of the two asymptotic regions of the wormhole geometry. The numerical experiments indicate that, as the charge approaches its critical value, the trumpet geometry approaches the extreme isotropic solution.

Felipe Medeiros

H. Oliveira

Numerical experiments with a regular charged black hole

We derive a compact analytic formula for a complete basis of conformally invariant tensor structures for three-point functions of conserved operators in arbitrary 4D Lorentz representations. The construction follows directly from a novel constraint equivalent to applying conservation conditions at each point: the leading terms in all OPE limits appear as symmetric traceless tensors. We derive this by lifting to a unified SU($\textit{m}$, $\textit{m}$|2$\textit{n}$) analytic superspace framework, where the conservation conditions are automatically solved and then reducing back to 4D CFT. The same method is also used for cases involving one non-conserved operator. This formalism further reveals a map of the counting of CFT tensor structures to that of finite-dimensional SU(2$\textit{n}$) representations, solved by Littlewood-Richardson coefficients. All results can be directly re-interpreted as three-point $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 4 superconformal tensor structures via the unified analytic superspace.

United Kingdom

Paul Heslop

Hector Puerta-Ramisa

A compact formula for conserved three-point tensor structures in 4D CFT