We initiate a systematic study on how to extract planar integrands of (supersymmetric) scattering amplitudes with $\textit{L}$ loops and $\textit{n}$ legs in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory from the recently proposed (bosonic) generating function for squared amplitudes with $\textit{N}$ := $\textit{n}$+$\textit{L}$ dual points; the latter enjoys a hidden permutation symmetry $\textit{S}$ and is given by a linear combination of weight-3 planar $\textit{f}$ -graphs that can be recast as bipartite graphs, which manifest important properties of ABJM amplitudes. We provide evidence that it contains sufficient information to reconstruct individual amplitudes, despite the absence of squared amplitudes at odd loops. The extraction of the four-point amplitude is already non-trivial and closely parallels the extraction of five-point amplitudes in $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM) from weight-4 $\textit{f}$-graphs: we comment on this similarity and provide new results for $\textit{n}$ = 4 ABJM loop integrand up to $\textit{L}$ = 6. For higher multiplicities, based on Yangian invariants (including BCFW building blocks for tree amplitudes) and an appropriate basis of planar dual conformal invariant(DCI) integrands, we disentangle six-point integrands up to two loops and eight-point tree amplitude from the squared amplitudes. Our results suggest that ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes, closely paralleling the role of $\textit{f}$-graphs in $$ \mathcal{N} $$ = 4 SYM.

China

Song He

United Kingdom

Yao-Qi Zhang

Loops and legs: ABJM amplitudes from $\textit{f}$-graphs

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.

Brazil

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

In this paper we consider the localization of the gravitino field on a codimension-one thick brane within the framework of $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) gravity. First, setting $$F(\phi ) = \phi $$ , we derive the potential functions for various parameters. Under appropriate coupling parameters, we can find the localized zero mode and some resonance states. Furthermore, we use these resonance states as initial data to investigate the evolution of the gravitino resonances. It can be observed that various parameters on the brane affect the evolution duration. We focus on comparing the localization behavior of the gravitino field on the brane for the cases with $$k=0$$ and $$k\ne 0$$ .

Xiang-Nan Zhou

Miao Wang

Zhi-Chao Duan

Localization of gravitino field on $\textit{f}$($\textit{R}$, $\textit{Q}$, $\textit{P}$) brane

In this paper, we investigate static, spherically symmetric traversable wormholes in the framework of symmetric teleparallel <italic>f</italic>( <italic>Q, T</italic>) gravity by considering the linear model <math altimg='si5.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi><mi>T</mi></mrow></math>. By assuming a constant redshift function to describe zero tidal force geometries, we derive the corresponding field equations and obtain an analytic solution for the shape function by adopting a radially dependent equation of state of the form <math altimg='si6.svg'><mrow><msub><mi>p</mi><mi>r</mi></msub><mo linebreak='goodbreak'>+</mo><mi>&#969;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mi>&#961;</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, with <math altimg='si7.svg'><mrow><mi>&#969;</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>A</mi><msup><mi>r</mi><mi>n</mi></msup></mrow></math>, where <italic>A</italic>&#8239;&gt;&#8239;0 and <italic>n</italic>&#8239;&gt;&#8239;0 are constants. The resulting wormhole configuration satisfies the fundamental geometric requirements, including the throat condition, the flare&#8211;out condition, and asymptotic flatness. The energy density remains positive and decreases with radius, while the null energy condition is violated only in the radial direction near the throat, indicating a localized exotic matter region. A Tolman&#8211;Oppenheimer&#8211;Volkoff analysis confirms that equilibrium is achieved through the balance between hydrostatic and anisotropic forces. Furthermore, the volume integral quantifier shows that the total amount of NEC&#8211;violating matter can be made arbitrarily small and confined close to the throat. The embedding diagrams support the geometric consistency of the solution. These results indicate that linear <italic>f</italic>( <italic>Q, T</italic>) gravity with a variable equation of state admits viable traversable wormhole solutions with minimized exotic matter content.

Morocco

Azerbaijan

M. Koussour

Saudi Arabia

H.M. ElKhair

Uzbekistan

N. Kurbonov

J. Rayimbaev

M.K.M. Ali

Static traversable wormholes supported by a variable equation of state in <italic>f</italic>( <italic>Q, T</italic>) gravity

One of the most popular competitors to the CDM paradigm as an explanation for the late-time acceleration of the universe is the modification of general relativity (GR), with models such as <italic>f</italic>( <italic>R</italic>) gravity among the main motivations. In this study, we consider an exponential <italic>f</italic>( <italic>R</italic>) gravity model as a possible extensions of the GR. The extra scalar degrees of freedom and their effects on the cosmic expansion and structure formation are continuously considered in this scenario. By combining the PPS, BBN, CC, DESI-DR2, and CMB datasets, we imposed limitations on this model. We performed a detailed statistical analysis of the free model parameter <italic>b</italic> together with the standard cosmological parameters. Our analysis yields values of <italic>H</italic> <inf>0</inf> that are slightly lower than those obtained in &#923;CDM, indicating no significant relaxation of the <italic>H</italic> <inf>0</inf> tension. In contrast, the model predicts systematically higher values of <italic>S</italic> <inf>8</inf>, leading to a moderate alleviation of the <italic>S</italic> <inf>8</inf> tension by up to &#8239;&#8764;&#8239;1.2 <italic>&#963;</italic> when late-time datasets are included. Overall, these results demonstrate that although the considered <italic>f</italic>( <italic>R</italic>) gravity model does not resolve all cosmological tensions simultaneously, it provides a consistent improvement in the description of large-scale structure formation.

India

Saurabh Verma

Archana Dixit

Anirudh Pradhan

M.S. Barak

Testing exponential <italic>f</italic>( <italic>R</italic>) gravity with CMB, DESI-DR2, and supernova data

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.

South Africa

Sudan Hansraj

Christian Boehmer

Ndumiso Buthelezi

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

We present quantitative results on the single-mass heavy-flavor contributions in the region of large virtualities <italic>Q</italic> 2 up to three-loop order to the unpolarized structure function <italic>F</italic> <inf>2</inf>( <italic>x, Q</italic> 2) and the polarized structure function <italic>g</italic> <inf>1</inf>( <italic>x, Q</italic> 2) for the first time. These results are relevant for precision QCD analyses of the World deep-inelastic data and the data taken at future colliders, such as the Electron&#8211;Ion Collider, since the scaling violations due to massless and massive Wilson coefficients are significantly different. In order to measure the strong coupling constant <math altimg='si19.svg'><mrow><msub><mi>&#945;</mi><mi>s</mi></msub><mrow><mo>(</mo><msubsup><mi>M</mi><mi>Z</mi><mn>2</mn></msubsup><mo>)</mo></mrow></mrow></math> and the twist-2 parton distribution functions consistently at highest precision, the next-to-next-to-leading order corrections have to be taken into account. We also provide a fast and precise public numerical code for the unpolarized and polarized massive Wilson coefficients in the asymptotic region.

Austria

J. Ablinger

Germany

A. Behring

J. Blümlein

A. De Freitas

A. von Manteuffel

C. Schneider

Switzerland

K. Schönwald

The three-loop single-mass heavy-flavor corrections to the structure functions <italic>F</italic> <inf>2</inf>( <italic>x, Q</italic> 2) and <italic>g</italic> <inf>1</inf>( <italic>x, Q</italic> 2)

In this work, we investigate the internal structure and physical features of compact stars in the background of modified gravity, specifically within <italic>f</italic>( <italic>R, G</italic>) gravity, where <italic>R</italic> represents the Ricci scalar and <italic>G</italic> denotes the Gauss&#8211;Bonnet invariant. The interior spacetime of the stellar configuration is described by the Kohler&#8211;Chao metric, which provides a suitable geometric representation for dense compact objects. Our analysis considers ten well-known compact star candidates, namely Her X-1, SAX J1808.4-3658, 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. To incorporate higher-curvature effects, the functional form of <italic>f</italic>( <italic>R, G</italic>) is decomposed into two independent contributions, <italic>f</italic> <inf>1</inf>( <italic>R</italic>) and <italic>f</italic> <inf>2</inf>( <italic>G</italic>), representing the Ricci scalar and Gauss&#8211;Bonnet sectors, respectively. For the <italic>R</italic>-dependent part, we adopt the Hu&#8211;Sawicki type model, while three different models, namely logarithmic and power-law models, are considered for the Gauss&#8211;Bonnet contribution. This reconstruction gives three distinct modified gravity models used to study the different features of compact stellar configurations. Using these models, we study the physical viability of the stellar structures by examining anisotropic pressure content, equilibrium scenario through the Tolman&#8211;Oppenheimer&#8211;Volkoff equation, energy conditions, and stability conditions. The obtained results demonstrate that the energy density, radial pressure, tangential pressure, and anisotropy remain well-behaved throughout the stellar interior for all considered stars. The analysis indicates that the proposed <italic>f</italic>( <italic>R, G</italic>) models together with the Kohler&#8211;Chao interior solution provide physically consistent and stable configurations for compact stars within the modified gravity framework.

Ahdab K. Althukair

Pakistan

M. Ilyas

Greece

Russia

Euaggelos E. Zotos

Kohler-Chao interior solutions for compact stellar objects in <italic>f</italic>( <italic>R, G</italic>) gravity

We examine the cosmological viability of two classes of nonminimally coupled <math altimg='si77.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math> gravity models, where the nonmetricity scalar <math altimg='si78.svg'><mi>Q</mi></math> induces an effective coupling between geometry and matter, with the aim of testing deviations from standard cosmology at the background level. The models considered include a linear, and an exponential nonminimal coupling. We constrain the background expansion histories using Type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, and Big Bang nucleosynthesis data, employing a combined <math altimg='si79.svg'><mrow><mi>&#967;</mi><mi>&#178;</mi></mrow></math> minimization technique to estimate cosmological and coupling parameters. We find that both models provide a stable description of the observed expansion history, yielding consistent values of the matter density parameter <math altimg='si9.svg'><msub><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mrow><mi>m</mi><mn>0</mn></mrow></msub></math> and the Hubble constant <math altimg='si7.svg'><msub><mi>H</mi><mn>0</mn></msub></math>&#8203; across datasets. In the linear model, the coupling parameters are constrained to positive values, while the deviation parameter remains compatible with zero, indicating behavior close to minimal coupling. The exponential model exhibits no statistically significant departure from minimal coupling, with background observations strongly constraining deviations from &#923;CDM. Overall, our results indicate that nonminimally coupled <math altimg='si77.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math> gravity models are consistent with current cosmological observations, with the data favoring parameter regions close to the &#923;CDM limit and showing no statistically significant evidence for deviations from standard cosmology at the background level.

Syria

Yahia Al-Omar

Nonminimally coupled <italic>f</italic>(Q) gravity under observational scrutiny

We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions $\textit{F}$ and $\textit{F}$ at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

Edoardo Spezzano

Tomas Ježo

Australia

Michael Klasen

United States

Peter Risse

France

Ingo Schienbein

Heavy-quark contributions to the DIS structure functions $\textit{F}$ 4 and $\textit{F}$ 5 at NLO in the ACOT scheme