One compelling way to probe dark matter is by looking for its gravitational effects on black holes. Inspired by the study of Cardoso et al. (Phys. Rev. D 105, 6, L061501 (2022)) on black holes in galaxies, this work investigates static, spherically symmetric black holes surrounded by Dekel-Zhao-type dark matter halos and influenced by a quintessential field. By adopting a double power-law profile, we derive explicit expressions for the cumulative mass, tangential velocity, and the modified metric, providing a coherent description of the horizon structure and thermodynamic properties. Depending on the core density, the spacetime may feature multiple horizons or even a naked singularity. Our analysis of null geodesics reveals that both dark matter and quintessence significantly affect photon trajectories and the resulting black hole shadow. By combining theoretical modeling with EHT observations of Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>, we place constraints on the halo density and quintessence parameter, directly connecting them to observable features. However, a stability analysis of circular photon orbits confirms that the photon sphere is inherently unstable, with its location and sensitivity strongly influenced by the surrounding matter. Finally, we analyze how the impact parameter <math altimg='si39.svg'><mover accent='true'><mi>b</mi><mo>&#732;</mo></mover></math> shapes photon trajectories around a black hole, determining the bending of null geodesics, the photon sphere location, and the event horizon structure, thereby illustrating the influence of spacetime geometry on light paths. This work highlights the intricate interplay between dark matter, quintessence, and black hole observables, bridging theoretical predictions with astrophysical measurements.

South Africa

Azerbaijan

A. Errehymy

Null geodesics and shadows of Dekel-Zhao-type dark matter black holes with a quintessential field: Constraints from EHT observations of M87 <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math> and Sgr A <math altimg='si14.svg'><msup><mrow /><mo>*</mo></msup></math>

Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Türkiye

Ali Övgün

Philippines

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

We study the ground states and left-excited states of the Ak−1 N=(2,0) little string theory. Via a theorem by Atiyah [1] , these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k) . The ground states, described by L2 -cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

Singapore

Meer Ashwinkumar

Jingnan Cao

Yuan Luo

Meng-Chwan Tan

Qin Zhao

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

In this paper, we will analyze a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such a deformed N=1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will only be preserved for a free theory and will be broken by the inclusion of interaction terms.

Canada

Mir Faizal

India

Mushtaq B. Shah

Anha Bhat

Prince A. Ganai

Zaid Zaz

Pakistan

Syed Masood

Jamil Raza

Raja Muhammad Irfan

Non-local deformation of a supersymmetric field theory

We perform a series of dimensional reductions of the 6d, N $$ \mathcal{N} $$ = (2, 0) SCFT on S 2 × Σ × I × S 1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S 1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S 2 × Σ × I , (ii) a further reduction on S 2 resulting in a complex Chern-Simons theory defined on Σ × I , with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S 2 and S 1 , and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I , which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an N $$ \mathcal{N} $$ = 2 supersymmetric theory on S 2 × I × S 1 , our results imply a 4d-2d duality between four-dimensional N $$ \mathcal{N} $$ = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

Petr Vasko

Four-dimensional N $$ \mathcal{N} $$ = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schrödinger–Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

France

Sanjib Dey

Chenguang Hou

Modification of Schrödinger–Newton equation due to braneworld models with minimal length

We explore the discovery potential of Higgs pair production at a 100 TeV collider via full leptonic mode. The same mode can be explored at the LHC when Higgs pair production is enhanced by new physics. We examine two types of fully leptonic final states and propose a partial reconstruction method, which can reconstruct some useful kinematic observables. It is found that the mT2 variable determined by this reconstruction method and the reconstructed visible Higgs mass are crucial to discriminate the signal and background events. It is also noticed that a new variable, denoted as Δm, which is defined as the mass difference of two possible combinations, is very useful as a discriminant. To examine the detector effects, we consider seven detector setups for a 100 TeV collider and investigate the changes in the sensitivity, and we find that lepton isolation and the minimal lepton Pt cut are crucial in order to reduce the integrated luminosity.

Belgium

Xiaoran Zhao

China

Qiang Li

Zhao Li

Qi-Shu Yan

Discovery potential of Higgs boson pair production through final states at a 100 TeV colliderSupported by Natural Science Foundation of China (11175251, 11305179, 11675185, 11475180, 11575005) The work of Q. Li and Q.S. Yan is partially supported by CAS Center for Excellence in Particle Physics (CCEPP), X. Zhao is partially supported by the European Union as part of the FP7 Marie Curie Initial Training Network MCnetITN (PITN-GA-2012-315877).

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger–Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger–Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger–Newton equation, a short distance modification of the Schrödinger–Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Short distance modification of the quantum virial theorem

In this paper, we study the restoration of gauge symmetry and up to half the supersymmetry ( N=(2,0) or N=(1,1) in two dimensions) for N=2 non-Abelian Chern–Simons theories in the presence of a boundary. We describe the boundary action which is a supersymmetric WZW model coupled to the bulk Chern–Simons theory. Unlike the N=1 case, higher supersymmetry ( N=(2,0) ) will endow the group manifold of the WZW model with a complex structure. Therefore, the N=(2,0) WZW model in our paper is constructed via a coset space Gc/G , where G is the same as the gauge group in the Chern–Simons action.

United Kingdom

Douglas J Smith

Gauge and supersymmetry invariance of N=2 boundary Chern–Simons theory

We study Ω-deformation of B-twisted gauge theories in two dimensions. As an application, we construct an Ω-deformed, topologically twisted five-dimensional maximally supersymmetric Yang-Mills theory on the product of a Riemann surface Σ and a three-manifold M , and show that when Σ is a disk, this theory is equivalent to analytically continued Chern-Simons theory on M . Based on these results, we establish a correspondence between three-dimensional N $$ \mathcal{N} $$ = 2 superconformal theories and analytically continued Chern-Simons theory. Furthermore, we argue that there is a mirror symmetry between Ω-deformed two-dimensional theories.

Italy

Junya Yagi

Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence