According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$\textit{G}$ gravity theory in which the effective gravitational constant $\textit{G}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $\textit{G}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $\textit{G}$ , which may ameliorate the “arrow of time” problem. We make some comparisons with the constant-$\textit{G}$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.

China

Chen-Hao Wu

Yen Ong

Cosmology with logarithmic corrected horizon entropy according to the generalized entropy and variable-$\textit{G}$ correspondence

We developed a unified framework based on a special (non-regular) embedding of the exceptional group $$E_6$$ in which the main stage of symmetry breaking chain realizes $$E_6\rightarrow G(2) \times SU(3)_A$$ . The exceptional factor $\textit{G}$(2) plays the role of a hidden strong sector, while $$SU(3)_A$$ acts as an ancestor of the electroweak gauge group. A minimal scalar sector is organized around a $$\textbf{650}$$ -based $$E_6$$ Higgs sector. Its $$G(2)\times SU(3)_A$$ components $$(\textbf{7},\textbf{1})$$ and $$(\textbf{1},\textbf{8})$$ implement the subsequent breaking steps $$G(2)\rightarrow SU(3)_C$$ and $$SU(3)_A\rightarrow SU(2)_L\times U(1)_A$$ . The $\textit{speciality}$ of this symmetry breaking establishes the feature of $\textit{darkness}$. Defining a hypercharge from the $$t_{8}$$ generator of $$SU(3)_A$$ is not sufficient to recover the exact Standard Model hypercharges and the correct Weinberg weak angle, leading to the necessity of an $$E_7$$ uplift which introduces only a proper additional $$U(1)_X$$ factor to fix the abelian sector. The special embedding naturally suppresses tree-level leptoquark couplings that typically mediate proton decay in regular grand unified theories. The scalar potential for the Higgs sectors has been constructed, deriving the heavy gauge-bosons spectrum and presenting a consistent one-loop running of the gauge couplings across the intermediate scales, which is shown to satisfy an $$E_6$$ unification. The exotic states are organized in $$E_7$$ -derived vectorlike pairs and are made ultraheavy, while a chirality-selecting projection keeps only the desired Standard Model zero modes. All non-Standard Model Higgs fields and $\textit{broken}$ massive vectors are found to be invisible to colliders searches. The $\textit{G}$(2) gluons ensemble confines into heavy dark glueballs with parametrically suppressed communication with $$SU(3)_A$$ and $$U(1)_X$$ sectors. Cosmological history is analyzed in details, including topological defects, inflation and reheating, demonstrating that monopole relics are naturally diluted. The resulting framework provides a minimal and internally consistent exceptional apparatus which includes the Standard Model and a dark matter sector which is secluded by the group-theoretic orthogonality.

Italy

Nicolò Masi

Toward a special $$E_6\rightarrow G(2) \times SU(3)_A$$ embedding for Standard Model and dark matter and an $$E_7$$ completion proposal

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

United States

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>

We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two nonspinning bodies in general relativity, accurate through fifth order in Newton’s constant and including second-order self-force effects. The calculation is carried out in the scattering-amplitude framework, combining the double-copy, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. To address a major computational bottleneck, we develop improved integration-by-parts algorithms that render calculations at this order tractable. The post-Minkowskian amplitude is presented as a series expansion, following the strategy used earlier in maximal supergravity. For the first self-force sector, which involves only polylogarithmic functions, we also provide a closed-form analytic expression. For the second self-force sector, as in earlier supergravity work, we find nontrivial cancellations among contributions related to integrals supported on Calabi-Yau geometry.

Zvi Bern

Enrico Herrmann

Switzerland

Radu Roiban

Michael S. Ruf

Russia

Alexander V. Smirnov

United Kingdom

Sid Smith

Mao Zeng

Scattering Amplitudes and Conservative Binary Dynamics at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>5</mn></msup><mo stretchy="false">)</mo></math> without Self-Force Truncation

We analyze quantum obstructions to classical infinite distance limits in four-dimensional string compactifications with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> supersymmetry. Such quantum effects signal a severe departure from the perturbative effective action and can be of considerable importance for string model building. Our focus is on the complex structure moduli space of type IIB orientifolds with O7/O3-planes and its F-theory description. In this first part of our analysis, we investigate the behavior of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math> corrections in infinite distance complex structure limits. Our main finding is that, depending on the location of the O7-plane, nonperturbative corrections in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math> can become unsuppressed, thus obstructing a perturbative type IIB description in the corresponding asymptotic region of the field space. In particular, this applies to large complex structure limits. To show this, we study the F-theory description of the type IIB orientifold, in which all pure <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math> corrections are encoded in the (classical) geometry of an elliptic Calabi-Yau fourfold. This <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math>-corrected moduli space is found to differ significantly from the classical moduli space. In extreme cases the classical infinite distance degeneration can be completely removed at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math>-corrected quantum level. The behavior of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>α</mi><mo>′</mo></msup></math> corrections, as well as implications for string model building, are discussed in a companion paper.

Germany

Lukas Kaufmann

Jeroen Monnee

Timo Weigand

Max Wiesner

Quantum obstructions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> infinite distance limits. I. <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math> obstructions

In this article, we present projected 95% C.L. limits on axion-like particle (ALP) couplings from ALP production at a future $$e^+e^-$$ collider operating at $$\sqrt{s} = 250~\text {GeV}$$ with integrated luminosity $$L = 0.5~\text {ab}^{-1}$$ . We constrain the effective couplings $$g_{\gamma \gamma }$$ , $$g_{Z\gamma }$$ , $$g_{ZZ}$$ , and $$g_{WW}$$ over the ALP mass range $$20~\text {GeV} \le m_a \le 100~\text {GeV}$$ , finding projected bounds at the level of $$\mathcal {O}(10^{-1})~\text {TeV}^{-1}$$ for $$g_{\gamma \gamma }/f_a$$ . Given that the latest muon anomalous magnetic moment measurement ( $$\Delta a_\mu $$ ) shows no statistically significant deviation from the Standard Model prediction, we reinterpret the ALP contributions to $$\Delta a_\mu $$ as a stringent consistency requirement. We then derive the corresponding allowed regions for $$g_{\gamma \gamma }$$ and the ALP–muon coupling $$C_{\mu \mu }$$ , and apply them to a fermionic dark matter scenario in which the relic density depends on both the dark matter mass $$m_\chi $$ and $$m_a$$ . The same parameter space is further constrained by Higgs signal strength measurements through $$h \rightarrow \gamma \gamma $$ and $$h \rightarrow Z\gamma $$ . A comparative analysis with existing experimental and theoretical bounds highlights the complementarity of $$\Delta a_\mu $$ , dark matter, and Higgs observables in restricting ALP couplings, demonstrating that even in the absence of a $$\Delta a_\mu $$ anomaly, these constraints provide essential guidance for viable ALP parameter space.

South Africa

India

Pramod Sharma

Soham Singh

Mukesh Kumar

Ashok Goyal

Comprehensive constraints on ALP couplings from future $$e^+e^-$$ colliders, muon $$g-2$$ , thermal dark matter and Higgs measurements

A numerical framework for approximating G <inf>2</inf>-structure 3-forms on contact Calabi&#8211;Yau manifolds is presented. The approach proceeds in three stages: first, existing neural network models are employed to compute an approximate Ricci-flat metric on a Calabi&#8211;Yau threefold. Second, using this metric and the explicit construction of a G <inf>2</inf>-structure on the associated 7-dimensional Calabi&#8211;Yau link in the 9-sphere, numerical approximations of the 3-form are generated on a large set of sampled points. Finally, a dedicated neural architecture is trained to learn the 3-form and its induced Riemannian metric directly from data, validating the learned structure and its torsion via a numerical implementation of the exterior derivative, which may be of independent interest.

Elli Heyes

Brazil

Edward Hirst

Henrique N. Sá Earp

Tomás S.R. Silva

Neural and numerical methods for G <inf>2</inf>-structures on contact Calabi&#8211;Yau 7&#8211;manifolds

We explore 3d $$ \mathcal{N} $$ = 4 theories arising from twisted compactification of 4d $$ \mathcal{N} $$ = 2 ($\textit{G}$, $\textit{G}$ ) Argyres-Douglas superconformal field theories (SCFTs), together with the 2d vertex operator algebras (VOAs) supported on the holomorphic boundary of their topologically twisted sector. Starting from the Coulomb branch BPS spectra of the ($\textit{G}$, $\textit{G}$ ) Argyres-Douglas theories, we develop a systematic and efficient method to obtain the ellipsoid partition functions of associated 3d theories using quiver mutations and wall-crossing invariants. This allows us to extract the modular data of the boundary VOAs, which are related to the Schur sectors of the 4d theories through the 4d SCFT/2d VOA correspondence. Our results provide a useful computational bridge between 4d SCFTs and 2d VOAs through interpolating 3d topological field theories.

South Korea

Minsung Kim

Sungjoon Kim

3D TFTs and boundary VOAs from BPS spectra of ($\textit{G}$, $\textit{G}$ ′) Argyres-Douglas theories

A modified gravitational model whose action is given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field, and its kinetic term is investigated as an extension of the gravitational sector including an additional dynamical degree of freedom. Within this framework, the causal structure of rotating cosmological solutions is analyzed by considering Gödel and Gödel-type spacetimes as background geometries used as theoretical probes of the model consistency. Different matter sources are examined, including a perfect fluid and scalar-field configurations. It is found that the standard Gödel metric is not compatible with the scalar sector of the theory unless the model reduces to the General Relativity limit. In contrast, Gödel-type geometries admit a wider class of solutions whose causal properties depend on the model parameters and on the matter content. In particular, perfect-fluid sources may lead to either causal or noncausal configurations, whereas scalar-field configurations constrain the geometry to the causal limit, preventing the formation of closed timelike curves, highlighting that the scalar field plays a nontrivial dynamical role distinct from that of a cosmological constant.

L. Evangelista

M. Silva

J. Moretti

A. Santos

Causality and its violation in $$f(R,\mathcal {L}_m,\phi ,g^{\mu \nu }\nabla _\mu \phi \nabla _\nu \phi )$$ gravity

The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term while the boundary term do not contribute to the dynamics. The advantage of the proposition is that the stellar structure equations are up to order two, thus the theory is not haunted by ghosts. We obtain explicitly the defining equations for the thermodynamical variables and the geometry for the pure quadratic case, since the linear case amounts to general relativity. In trying to establish the vacuum geometry associated with the theory it turns out that two possible metrics emerge through the vanishing of the energy-momentum tensor. Next, we analyse the isotropy equation and make the observation that it is autonomous. It is rare that this happens in astrophysical modelling. This behaviour prompted the use of dynamical systems to understand the stability properties of fixed points or invariant submanifolds. It was necessary to choose a gauge in order to split the autonomous equation into a system from which we could plot a phase portrait and deduce the stability of solution trajectories. We find that the invariant submanifolds were generally stable with nearby paths approaching them.

Sudan Hansraj

Christian Boehmer

Ndumiso Buthelezi

Dynamical systems approach to stellar modelling in $\textit{f}$($\textit{G}$, $\textit{B}$) gravity