We consider a general class of large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1 in a Hamiltonian approach. We show that by using lightcone quantization and the $\textit{N}$ → ∞ limit, we can diagonalize the Hamiltonian exactly and construct the eigenstates, spectral density, S-matrix, and form factors for the theory. For concreteness, we mainly focus on QED at large $\textit{N}$ as an explicit example. We comment on extending the approach to finite $\textit{N}$ calculations.

United States

A. Fitzpatrick

Anastasiia Novikova

Noah Ring

Hamiltonian truncation of large $\textit{N}$ $\textit{f}$ QED and large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1

<p>We investigate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext>−</mtext><mn>1</mn><mi>F</mi></mrow></math> mixing in charmonium, focusing on the close-in-mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo></math> states. The conventional tensor force yields negligible mixing, motivating the inclusion of coupled-channel effects. Our unquenched calculation reveals sizable mixing angles of 7.5° and 15.4°. We predict the corresponding two-photon and two-gluon decay widths as key observables for experimental verification. Additionally, we discuss the production of these two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext>−</mtext><mn>1</mn><mi>F</mi></mrow></math> mixed states of charmonium via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi></math> fusion. Current data are insufficient to determine the mixing, highlighting the need for precise future measurements to resolve this aspect of charmonium spectroscopy.</p>

China

Peng-Yu Sun

Tian-Le Gao

Zi-Long Man

Xiang Liu

Proposed mixing between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math> wave charmonia

We discuss the reconstruction of scalar field potential necessary to witness inflation at the very early phase of the Universe. A minimally coupled inflaton field is considered along with a modified teleparallel gravity where the action contains a function of torsion. Reconstruction mechanism in a most general way is discussed. Constant roll inflation is imposed upon the field equations to simplify the reconstruction procedure. Considering a functional form of $\textit{f}$($\textit{T}$), we obtained the effective scalar field potential and Hubble parameter in an analytic manner.

India

B. Mishra

S. Tripathy

Constant roll inflation and reconstruction of scalar field potential in $\textit{f}$($\textit{T}$) gravity

In this study, we explore the cosmological evolution of the Universe in the framework of covariant $\textit{f}$($\textit{Q}$) gravity, with a coupling function that evolves dynamically in proportion to the Hubble parameter. Two specific forms of the function are examined: a power-law model and a logarithmic model. By rewriting the cosmological field equations as an autonomous dynamical system, we determine and classify the corresponding critical points and analyze their stability. Our results show that both models are able to reproduce the sequence of cosmic evolution, including radiation, matter, and dark energy-dominated eras, along with the transitions between them. The physical properties at each critical point are described using key cosmological quantities such as the total EoS parameter, density parameters, and the deceleration parameter. The stability of the non-hyperbolic critical point is analyzed through center manifold theory. In addition, we present phase space trajectories along with the stability behavior of each critical point. The evolution plots for the density parameters of radiation, matter, and dark energy, along with the Equation of State (EoS) parameter for the total, are illustrated for further analysis. Overall, the analysis suggests that the $\textit{f}$($\textit{Q}$) models considered here, within the context of covariant formulation, provide a consistent description of cosmic evolution and offer a promising approach to explaining the late-time acceleration of the Universe.

S. Narawade

S. Kadam

Dynamical analysis of the covariant $\textit{f}$($\textit{Q}$) gravity models

We investigate the direct $\rm CP $ violation in the decay $ D^\pm \to \pi^\pm \pi^+ \pi^- $ incorporating the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism. The integrated mixing intensities $ \overline \xi_{fa} $ and $ \overline \xi_{af} $ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $ \pi^+\pi^- $ pair lies near the $ f_0(980) $ resonance, this isospin-breaking mechanism can enhance the $\rm CP $ asymmetry. The enhancement is particularly pronounced when the $ f_0(980) $ carries a significant $ n\bar{n} $ quark component and the $ f_0(980) $ and $ \sigma(600) $ mixing angle is approximately $ 26^\circ $ . After accounting for non-factorizable effects, we find these corrections tend to partially cancel the leading-order contributions, resulting in a suppression of the $\rm CP $ violations relative to the naive factorization predictions. It is emphasized that the $ a_0^0(980) $ - $ f_0(980) $ mixing mechanism should be taken into account in both theoretical and experimental studies of $\rm CP $ violation in $\textit{B}$ or $\textit{D}$ meson decays.

Shi-Ji Cao

Jing-Juan Qi

Yi-Fan Zhao

Chao Wang

Zhen-Yang Wang

Xin-Heng Guo

Direct CP violation in ${ {\boldsymbol D}^{\bf\pm }\to {\boldsymbol\pi}^{\bf\pm} {\boldsymbol\pi}^{\bf +} {\boldsymbol\pi}^{\bf -}} $ with ${{\boldsymbol a}_{\bf 0}^{\bf 0}{\bf (980)-}{\boldsymbol f}_{\bf 0}{\bf (980)}} $ mixing * Supported by the National Natural Science Foundation of China (12405115, 12105149, 11805153, 12275024), and the High-Level Scientific Research Fund of Ningbo University (GJPY2026032)

In this work, we investigate the cosmological consequences of an effective ΛCDM model emerging from the more general <italic>f</italic>( <italic>Q, T</italic>) gravity theory under the special equation-of-state condition <math altimg='si20.svg'><mrow><mi>&#961;</mi><mo linebreak='goodbreak'>+</mo><mi>p</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Under this limit, the field equations yield the constraint <math altimg='si21.svg'><mrow><mi>F</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>C</mi></mrow></math>, implying that the function <math altimg='si22.svg'><mrow><mi>F</mi><mo linebreak='goodbreak'>=</mo><msub><mi>f</mi><mi>Q</mi></msub></mrow></math> becomes purely dependent on the non-metricity scalar <italic>Q</italic>, and the background evolution mimics that of the standard &#923;CDM model. We derive the resulting functional forms of <italic>f</italic>( <italic>Q</italic>), obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we perform a background-level parameter estimation for <italic>H</italic> <inf>0</inf> and &#937; <inf><italic>m</italic></inf>, and evaluate the derived parameter <italic>S</italic> <inf>8</inf> (anchored to the Planck baseline <italic>&#963;</italic> <inf>8</inf>) using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A dual-pipeline analysis is carried out using conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling alongside a machine-learning based Artificial Neural Network (ANN) emulator deployed as a complementary consistency check. We demonstrate that the ANN approach successfully emulates the continuous parameter space with high computational efficiency, yielding results in close agreement with the standard MCMC likelihood framework. Because the background evolution strictly mimics the standard &#923;CDM paradigm, the model successfully reproduces recent observational trends and recovers standard parameter constraints without dynamically resolving the baseline <italic>H</italic> <inf>0</inf> and <italic>S</italic> <inf>8</inf> tensions. Our results indicate that effective &#923;CDM scenarios derived from <italic>f</italic>( <italic>Q, T</italic>) gravity provide a viable and consistent with recent observational data.

Anil Kumar Yadav

S.H. Shekh

Kazakhstan

N. Myrzakulov

Anirudh Pradhan

Saudi Arabia

Nafis Ahmad

A.M. Alshehri

Effective ΛCDM model emerging from <italic>f</italic>( <italic>Q, T</italic>) under a special EOS limit in symmetric cosmology with Bayesian and ANN observational constraints

In this work, we investigate the physical viability and structural properties of compact stars within the framework of modified gravity, specifically <italic>f</italic>( <italic>R</italic>) gravity. Three distinct functional forms of the gravitational Lagrangian are considered, namely <math altimg='si8.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>R</mi><mn>2</mn></msup></mrow></math>, <math altimg='si10.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>R</mi><mn>2</mn></msup><mrow><mo>(</mo><mn>1</mn><mo linebreak='badbreak'>+</mo><mi>&#947;</mi><mi>R</mi><mo>)</mo></mrow></mrow></math>, and <math altimg='si12.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>R</mi><mrow><mo stretchy='true'>(</mo><msup><mi>e</mi><mrow><mo>&#8722;</mo><mi>R</mi><mo>/</mo><mi>&#947;</mi></mrow></msup><mo linebreak='badbreak'>&#8722;</mo><mn>1</mn><mo stretchy='true'>)</mo></mrow></mrow></math>, which allow us to explore both polynomial and exponential corrections to General Relativity. The interior spacetime is modeled using a static and spherically symmetric anisotropic fluid distribution, and the corresponding modified field equations are solved to obtain the energy density, radial pressure, and tangential pressure profiles. To assess the astrophysical relevance of the proposed models, we apply them to ten observed compact stellar candidates, namely Her X-1, SAX J1808.4&#8211;3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. The obtained solutions are examined through several physical acceptability criteria, including regularity conditions, energy conditions, causality, equilibrium via the generalized Tolman&#8211;Oppenheimer&#8211;Volkoff equation, and stability analyses. Furthermore, key observable quantities such as mass&#8211;radius relations, compactness, surface redshift, and anisotropy are discussed in detail for each model. Our results indicate that all three <italic>f</italic>( <italic>R</italic>) gravity models can support realistic and stable astrophysical compact star configurations, with noticeable deviations from General Relativity, particularly for higher curvature regimes, suggesting that modified gravity effects may play a significant role in describing ultra-dense stellar objects.

Shah Muhammad

Azerbaijan

Pakistan

M. Ilyas

Greece

Russia

Euaggelos E. Zotos

Physical viability of dark energy compact stars in <italic>f</italic>( <italic>R</italic>) gravity using Durgapal-Fuloria solutions

We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $\textit{F}$ (4). The geometry is a product of complexified maximally symmetric spaces $$ {\mathcal{M}}_{6\mathbb{C}} $$ and $$ {\mathcal{M}}_{2\mathbb{C}} $$ warped over a complexified surface Σ . We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB and IIB , as well as theories with 3, 5, 7 and 9 time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of $\textit{F}$ (4), whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $$ {\mathcal{M}}_6 $$ and $$ {\mathcal{M}}_2 $$ warped over a Riemann surface Σ, with various signatures. The real solutions include, among others, known $\textit{AdS}$ × $\textit{S}$ × Σ and $\textit{AdS}$ × $\textit{S}$ × Σ solutions to standard Type IIB as well as new solutions of the form $\textit{dS}$ × $\textit{S}$ × Σ in Type IIB . There are no real forms of the complex solutions with $$ \mathbf{\mathfrak{so}}\left(7;\mathbb{R}\right) $$ ⨁ $$ \mathbf{\mathfrak{so}}\left(3;\mathbb{R}\right) $$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from $\textit{dS}$ × $\textit{S}$ × Σ to $\textit{S}$ × $\textit{S}$ × Σ within complex Type IIB, in connection with holography for the polarized IKKT model.

Eric D’Hoker

Michael Gutperle

Belgium

Christoph Uhlemann

Exact solutions to complex Type IIB supergravity for complex superalgebra $\textit{F}$ (4) and its real forms

In this work, we investigate the equilibrium structure of white dwarfs within the covariant formulation of symmetric teleparallel <italic>f</italic>( <italic>Q</italic>) gravity, in which gravity is described by the nonmetricity scalar <italic>Q</italic> instead of spacetime curvature. We consider static and spherically symmetric stellar configurations composed of cold, fully degenerate electron matter and adopt a quadratic form of the gravitational Lagrangian, <math altimg='si7.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>Q</mi><mn>2</mn></msup></mrow></math>, where <italic>&#945;</italic> quantifies deviations from general relativity. The corresponding modified stellar structure equations are solved numerically in conjunction with the Chandrasekhar equation of state. We examine the impact of the parameter <italic>&#945;</italic> on the internal structure and global properties of white dwarfs, including the radial profiles of the metric potentials, pressure, density, nonmetricity scalar, and enclosed mass, as well as the mass&#8211;radius relation. While negative values of <italic>&#945;</italic> were explored, they lead to unstable or nonphysical configurations at high densities; therefore, the analysis is restricted to non-negative values of <italic>&#945;</italic>. Our results show that nonmetricity corrections produce significant deviations from the general relativistic predictions in the high-density regime. In particular, increasing <italic>&#945;</italic> modifies the equilibrium configurations and leads to a reduction in the maximum mass relative to the Chandrasekhar limit, accompanied by corresponding changes in the stellar radius and interior profiles. For <math altimg='si12.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mn>5</mn><mo linebreak='goodbreak'>&#215;</mo><msup><mn>10</mn><mn>18</mn></msup><mspace width='0.16em' /><mrow><msup><mtext>cm</mtext><mn>2</mn></msup></mrow></mrow></math>, we obtain a maximum mass <math altimg='si13.svg'><mrow><msub><mi>M</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>1.3519</mn><mspace width='0.16em' /><msub><mi>M</mi><mo>&#8857;</mo></msub></mrow></math> and radius <math altimg='si14.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>2228.85</mn><mspace width='0.16em' /><mtext>km</mtext></mrow></math>, which are consistent with the observational constraints of the ultra-massive white dwarf ZTF J1901+1458. These findings suggest that white dwarfs may serve as complementary astrophysical probes for testing the viability of <italic>f</italic>( <italic>Q</italic>) gravity in the strong-field regime.

Rajasmita Sahoo

White dwarf structure in <italic>f</italic>( <italic>Q</italic>) gravity

We ask whether two classical time-machine geometries, the Ori (2005) compact-vacuum-core metric and the Ahmed (2018) four-dimensional generalisation of Misner space, remain admissible exact solutions when the gravitational sector is enlarged to the recently proposed $$f(R,\mathcal {L}_{m},\Phi ,X)$$ class, an extension of $$f(R,\mathcal {L}_{m})$$ that couples curvature, the matter Lagrangian density, a scalar field $$\Phi $$ , and its kinetic invariant $$X = g^{\mu \nu }\nabla _{\mu }\Phi \nabla _{\nu }\Phi $$ . Working with the explicit model $$f = R + \mathcal {L}_{m} + (\lambda /2)\,X$$ and a vanishing scalar potential, we compute the curvature invariants, the modified field equations, and the effective stress-energy components produced by the harmonic scalar profile $$\Phi (x,y) = a(x^{2}-y^{2})/2$$ in both backgrounds. The Ricci scalar vanishes for the Ori metric and obeys $$R = e^{f}(f_{,xx}+f_{,yy})$$ for the Ahmed metric; the kinetic invariant takes the explicit forms $$X = a^{2}(x^{2}+y^{2})$$ and $$X = a^{2}e^{f}(x^{2}+y^{2})$$ , respectively. Both metrics solve the field equations of the modified theory with anisotropic matter sources, and the chronology-violating regions $$g_{zz}<0$$ (Ori) and $$g_{\psi \psi }<0$$ (Ahmed) survive the modification. Energy-density profiles measured by a closed-timelike-curve observer match those measured by a static observer outside the chronology horizon, so the additional scalar degree of freedom in $$f(R,\mathcal {L}_{m},\Phi ,X)$$ gravity does not enforce a chronology-protection mechanism in either background. The conclusion mirrors the parallel result for the Li time-machine and supplies a consistency test for scalar-extended modified gravity in non-globally-hyperbolic settings.

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Türkiye

İzzet Sakallı

Are Petrov type-N and D spacetimes admitting CTCs valid in $$f(R,\mathcal {L}_m,\Phi ,X)$$ gravity?