We generalize the explicit construction of fields in orbifolds of products of <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math> minimal models, developed by A. Belavin, V. Belavin and S. Parkhomenko to include minimal models with D and E-type modular invariants. It is shown that spectral flow twisting by the elements of admissible group <italic>G</italic> <inf>adm</inf>, which is used in the construction of the orbifold, is consistent with the nondiagonal pairing of D and E-type minimal models. We obtain the complete set of fields of the orbifold from the mutual locality and other requirements of the conformal bootstrap. The collection of mutually local primary fields is labeled by the elements of dual group <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math>. The permutation of <italic>G</italic> <inf>adm</inf> and <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math> is given by the mirror spectral flow construction of the fields and maps the space of states of the original <italic>G</italic> <inf>adm</inf> orbifold onto the space of states of <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math> orbifold. We show that this transformation is by construction a mirror isomorphism of spaces of states. Thus, mirror isomorphism of states is built into the construction. We illustrate our approach for the orbifolds of <math altimg='si4.svg'><mrow><msub><mi mathvariant='bold'>A</mi><mn>2</mn></msub><msubsup><mi mathvariant='bold'>E</mi><mn>7</mn><mn>3</mn></msubsup></mrow></math> model.

Russia

Boris Eremin

Sergej Parkhomenko

Explicit construction of states in orbifolds of products of <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> superconformal ADE minimal models

This work employs the minimal geometric deformation decoupling scheme to derive interior stellar solutions in the background of an electrically charged BTZ ansatz as a seed metric in three dimensions. In this respect, we impose two different equations of state to determine the deformation function and the new material contributions emerging from the additional field source. Furthermore, we describe the finiteness of all thermodynamic quantities of the presented stellar solutions, including the effective thermodynamical quantities, for varying values of the deformation parameter and total electric charge. We explore the new interior astrophysical solutions in three-dimensional gravity by analyzing the charged BTZ metric, admitting circular symmetry through the principles of geometric deformation. This study examines the impact of radial-metric deformation on the charged BTZ geometry and underscores the importance of stellar decoupling within the context of electrically charged dense distributions. It is shown that new physically acceptable solutions by incorporating any known three-dimensional spacetime as the isotropic basis are possible, which in turn enable one to analyze the quantum effects due to low degrees of freedom at lower dimensions.

Pakistan

Z. Yousaf

Japan

Kazuharu Bamba

Saudi Arabia

Mansoor Alshehri

S. Khan

Azerbaijan

M.Z. Bhatti

Physical features of geometrically deformed anisotropic charged three-dimensional BTZ black holes

In this paper, we have tested the non-unitary mixing hypothesis with the latest data from NO <italic>&#957;</italic>A and T2K experiments. We have also analysed their combined data. We have provided the best-fit values of the standard and non standard parameters after the analysis. 90% limits on the non-unitary mixing parameters have also been provided. The constraints on unitary violation is stronger, compared to the constraints obtained from previous data from NO <italic>&#957;</italic>A and T2K. The tension between NO <italic>&#957;</italic>A and T2K at the 1&#8201; <italic>&#963;</italic> for normal mass hierarchy can be reduced for non-unitary mixing due to <italic>&#945;</italic> <inf>10</inf>, albeit for a value of | <italic>&#945;</italic> <inf>10</inf>| larger than the present global 90% limit. Additionally a study of the future sensitivity of NO <italic>&#957;</italic>A, T2K and DUNE has been provided.

Canada

Xin Yue Yu

Zishen Guan

Ushak Rahaman

Nikolina Ilic

Update on non-unitary mixing in the recent NO <italic>&#957;</italic>A and T2K data

We discuss in this paper the lattice discretizations of all topological defect lines (TDLs) for diagonal, minimal CFTs, using integrable restricted solid-on-solid (RSOS) models. For these CFTs, the TDLs can be labeled by the Kac labels. In the case of (1, <italic>s</italic>) TDLs, lines that are exactly topological on the lattice can be obtained using the centralizer of the underlying Temperley-Lieb algebra, all the other lines become topological in the continuum limit only. Our general construction relies on insertions of rows/columns of faces with modified spectral parameters, and can therefore be studied using integrability techniques. We determine the regions of spectral parameters realizing the different ( <italic>r, s</italic>) TDLs, and in particular calculate analytically all the associated eigenvalues (and degeneracy factors). We also show how fusion of TDLs can be obtained from fusion hierarchies in the algebraic approach to the Bethe-ansatz. All our results are checked numerically in detail for several minimal CFTs.

United States

Madhav Sinha

Brazil

Thiago Silva Tavares

Ananda Roy

France

Hubert Saleur

Integrability and lattice discretizations of all topological defect lines in minimal CFTs

We investigate exact charged and uncharged black hole solutions in a (2+1)-dimensional spacetime within the framework of quadratic form of <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> symmetric teleparallel gravity, where <math altimg='si15.svg'><mi mathvariant='double-struck'>Q</mi></math> is the non-metricity scalar. By adopting spherical symmetry and considering both vanishing and non-vanishing electromagnetic fields, we derive new classes of black hole solutions and analyze their geometric and physical properties. The study demonstrates that the inclusion of quadratic corrections in the gravitational Lagrangian significantly modifies the structure of solutions, producing deviations from the standard BTZ geometry. Invariants such as curvature and non-metricity scalars are calculated to classify the singularity structure and spacetime behavior. Thermodynamic quantities, including Hawking temperature, entropy, and heat capacity, are computed, showing consistency with the first law of black hole thermodynamics. Furthermore, we examine the geodesic motion of test particles and derive the effective potential to explore the stability of photon orbits. A notable outcome is the identification of weaker black hole singularities in comparison to General Relativity, attributed to the non-metricity corrections. The possibility of multi-horizon configurations is also explored. This study provides a comprehensive analysis of the gravitational, thermodynamic, and dynamical features of lower-dimensional black holes in <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity and highlights their distinct characteristics with respect to General Relativity.

Egypt

Gamal G.L. Nashed

Italy

Salvatore Capozziello

Stable black holes in lower dimensional <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> non-metric gravity

In the present paper we consider the usage of associative Yang-Baxter equations in the theory of classical and quantum <italic>ABCD</italic> algebras [1]. Classical and quantum associative analogs of the generalized Fredel-Maillet equations for <italic>ABCD</italic> tensors [2, 3] are found. Two classes of examples &#8212; rational and trigonometric &#8212; of classical and quantum <italic>ABCD</italic> tensors satisfying these equations are considered in details.

Ukraine

T. Skrypnyk

On ABCD algebras and associative Yang-Baxter equations

We generate a radiating star in Einstein-Gauss-Bonnet (EGB) gravity for spacetime dimension <math altimg='si10.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>5</mn></mrow></math> and a shear-free geometry. The temporal boundary condition contains curvature corrections from the Lovelock tensor and reduces to the general relativity limit. A detailed analysis of the model indicates that the temporal evolution of the star is qualitatively different from general relativity. Firstly, the phase plane analysis shows that the phase trajectories are less constrained due to the Gauss-Bonnet parameter. Secondly, separable metrics in EGB gravity imply that shear-free collapse generates anisotropic pressures; the corresponding isotropic configurations in general relativity cannot arise because of the EGB curvature corrections. Remarkably it is possible to find radiating models in pure EGB gravity which involve Lambert functions. The symmetries associated with the EGB boundary condition have a structure different from general relativity. The self-similar nature of general relativity is lost in pure EGB gravity. Consequently, radiating bodies in EGB gravity possess distinct geometrical and physical features.

South Africa

Sunil D. Maharaj

Byron P. Brassel

Sumeekha Singh

Keshlan S. Govinder

A radiating star in Einstein-Gauss-Bonnet gravity

The Khovanov-Rozansky (KR) link polynomial is a certain <italic>t</italic>-deformation of Wilson loops in 3-dimensional <italic>SU</italic>( <italic>N</italic>) Chern-Simons topological field theory, believed to be an observable in the refined Chern-Simons theory, probably described in terms of 4d or 5d QFT and related by a certain procedure to the triply-graded link &lt;&lt;superpolynomial&gt;&gt;. This link invariant was originally introduced by M. Khovanov and L. Rozansky through a sophisticated matrix factorization technique based on the bicomplex structure, which depends on entire link diagrams and rapidly increases in complexity with the growth of a link. However, for particular link diagrams a local reduction is possible, allowing to eliminate vertices in a regular way, and thus, simplifying the KR polynomial and making it as simple as the Khovanov polynomial in the <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> case. In particular, for a distinguished family of bipartite links, matrix factorization defined on MOY diagrams reduces just to planar cycles &#8211; very similar to the original Kauffman-Khovanov construction at <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> for the Jones polynomial and its <italic>t</italic>-deformation. In the bipartite case, this can be done for any <italic>N</italic>. We make a further step of simplification and reduce from cohomology factor-rings in even variables crucially depending on a MOY diagram to vector spaces spanned by odd variables, so that the initial bicomplex of matrix factorizations becomes a monocomplex of just tensor products of <italic>N</italic>-dimensional vector spaces. We also find the explicit form of three universal morphisms which were guessed in a recent paper on this subject. Universality means independence of the other edges of the diagram, and we explain why this works in this particular case.

E. Lanina

R. Stepanov

Khovanov-Rozansky matrix factorization reduction for bipartite links

With the recent revival of interest in the FLPR model, novel features have been reported in the literature. A connection between those new feautures and QCD, involving the Gribov problem, is explored. We investigate the FLPR model in a recently proposed framework of BRST-related symmetries and perform its full functional quantization as a gauge invariant system taking into account the Gribov ambiguities and produce a consistent generating functional which can be used as a starting point for the Gribov-Zwanziger-Sorella program. We obtain a family of BRST-related transformations generated by the discrete group of symmetries of the action. We show that gauges possessing Gribov ambiguities lead to a violation of the initial discrete group of symmetries of the gauge-fixed action. The obtained results shed light into similar issues in QCD by the corresponding association of variables and fields between the two systems.

India

Bhabani Prasad Mandal

Sumit Kumar Rai

Ronaldo Thibes

On BRST-related symmetries in the FLPR model with Gribov ambiguities

The observed matter–antimatter asymmetry of the Universe remains a fundamental challenge in modern physics. In this work, we explore gravitational baryogenesis within the framework of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity, where the gravitational Lagrangian depends on both the torsion scalar <italic>T</italic> and the matter Lagrangian <italic>L<inf>m</inf></italic>. We consider three representative models and examine their ability to generate the observed baryon-to-entropy ratio. Our analysis shows that couplings involving both torsion and the matter Lagrangian, <math altimg='si35.svg'><mrow><msub><mi>&#8706;</mi><mi>&#956;</mi></msub><mrow><mo>(</mo><mo>&#8722;</mo><mi>T</mi><mo linebreak='badbreak'>&#8722;</mo><mfrac><msub><mi>L</mi><mi>m</mi></msub><msub><mi>L</mi><mn>0</mn></msub></mfrac><mo>)</mo></mrow></mrow></math>, can successfully account for the baryon asymmetry for decoupling temperatures in the range 10 <sup>12</sup>&#8211;10 <sup>14</sup>&#8201;GeV, while remaining consistent with small deviations from General Relativity. These results highlight the capacity of <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity to provide novel mechanisms for baryogenesis, demonstrating that the interplay between torsion and matter-sector contributions can naturally generate the observed asymmetry. The framework also remains compatible with late-time cosmological evolution, offering a unified setting for early- and late-time dynamics.

Portugal

Daniel F P Cruz

David S. Pereira

Francisco S N Lobo

Gravitational baryogenesis in <italic>f</italic>( <italic>T, L<inf>m</inf></italic>) gravity