In this letter, we investigate the deformation of the ModMax theory, as a unique Lagrangian of non-linear electrodynamics preserving both conformal and electromagnetic-duality invariance, under <math><mi>T</mi><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>-like flows. We will show that the deformed theory is the generalized non-linear Born-Infeld electrodynamics. Being inspired by the invariance under the flow equation for Born-Infeld theories, we propose another <math><mi>T</mi><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>-like operator generating the ModMax and generalized Born-Infeld non-linear electrodynamic theories from the usual Maxwell and Born-Infeld theories, respectively.

Iran

H. Babaei-Aghbolagh

Komeil Babaei Velni

Davood Mahdavian Yekta

H. Mohammadzadeh

Emergence of non-linear electrodynamic theories from -like Deformations

Recently, the ModMax theory has been proposed as a unique conformal nonlinear extension of electrodynamic theories. We have shown in [H. Babaei-Aghbolagh et al., Phys. Lett. B 829, 137079 (2022).] that this modification can be reproduced by using a marginal <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>-like deformation from pure Maxwell theory. Further, it was shown that this deformation is solvable by applying a perturbative approach. In this paper, we will investigate a similar marginal <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>-like deformation for a general two-dimensional scalar field theory. It is shown that employing an irrelevant <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> operator on this marginal scalar theory will produce a generalized Nambu-Goto action of this scalar theory which is a Born-Infeld-like action in two dimensions. Using a similar prescription for a two-dimensional theory with multiple scalar fields, we show that the marginal <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>-like deformation yields a ModMax-like Lagrangian and then the irrelevant operator produces a generalized scalar ModMax action.

Marginal <math><mrow><mi>T</mi><mover><mrow><mi>T</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>-like deformation and modified Maxwell theories in two dimensions

The relationship between thermodynamics and the Lloyd bound on the holographic complexity for a black hole has been of interest. We consider <math><mrow><mi>D</mi></mrow></math> dimensional anti–de Sitter black holes with hyperbolic geometry as well as black holes with momentum relaxation that have minimum values for the temperature and the mass. We will show that the singular points of the thermodynamic curvature of the black holes, as thermodynamic systems, correspond to the zero points of the action and volume complexity at the Lloyd bound. For such black holes with a single horizon, the rates of growth of the complexity of volume and the complexity of action at minimum mass and minimum temperature are zero, respectively. We show that the thermodynamic curvature diverges at these minimal values. Because of the behavior of the growth rate of the action complexity and thermodynamic curvature at minimum temperature, we propose the growth rate of the action complexity as an order parameter of the black holes as the thermodynamic systems. Also, we derive the critical exponent related to the thermodynamic curvature in different dimensions.

Hosein Mohammadzadeh

Thermodynamic geometry and complexity of black holes in theories with broken translational invariance

We employ the “complexity equals action” conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in (<math><mi>d</mi><mo>+</mo><mn>1</mn></math>)-dimensional bulk spacetime with <math><mi>d</mi><mo>−</mo><mn>1</mn></math> massless scalar fields, which is called Einstein-Maxwell-axion theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt patch saturates the corresponding Lloyd bound at the late-time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of the relaxation parameter <math><msub><mi>β</mi><mrow><mi>max</mi></mrow></msub></math> where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A nonlinear contribution of the axion field kinetic term in the context of the <math><mi>k</mi></math>-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model.

Holographic complexity for black branes with momentum relaxation

In the context of guage/gravity duality, we investigate the central charges of a number of 2-dimensional conformal field theories (CFTs) that might live on the boundary of some 3-dimensional (3D) toy models of gravity, from the thermodynamics aspect of the black holes. For many black hole solutions, the entropy product of the inner Cauchy and outer event horizons is universal (mass independent). It is proposed that for these solutions, the central charges of the left- and right-moving sectors of the dual CFTs should be the same and one may read the central charges from the universal entropy product. This provides strong motivations for investigating this prescription for BTZ and Warped $$\hbox {AdS}_{{3}}$$ <math><msub><mtext>AdS</mtext><mn>3</mn></msub></math>  black holes in a number of 3D gravity theories and we will show that the proposal works truly. One striking result of our analysis is that if the entropy product is not universal in any theory of 3D gravity, then the left and right central charges are not equal.

Hanif Golchin

Central charges from thermodynamics method in 3D gravity

In this letter we investigate the throttling process of the charged Anti-de Sitter (AdS) black holes in the rainbow gravity. In the extended phase space of these black holes, the cosmological constant plays the role of a varying thermodynamic pressure and the black hole mass is identified with the thermodynamic enthalpy. We derive exact expressions for the Joule-Thomson coefficient and the inversion temperature in terms of black hole parameters and constants of rainbow gravity analytically, and then perform a numerical analysis for the isenthalpic and inversion curves of charged AdS black holes. Our calculations show all quantities are sensitive to rainbow parameter η. We also discuss the isenthalpic curves for different values of the black hole mass.

Arezoo Hadikhani

Türkiye

Özgür Ökcü

Joule-Thomson expansion of charged AdS black holes in rainbow gravity

We investigate the asymptotic structure of the three dimensional Warped Anti-de Sitter (WAdS$_{3}$) black holes in the Bergshoeff–Hohm–Townsend (BHT) massive gravity using the canonical Hamiltonian formalism. We define the canonical asymptotic gauge generators, which produce the conserved charges and the asymptotic symmetry group for the WAdS$_{3}$ black holes. The attained symmetry group is described by a semi-direct sum of a Virasoro and a Kač–Moody algebra. Using the Sugawara construction, we obtain a direct sum of two Virasoro algebras. We show that not only the asymptotic conserved charges satisfy the first law of black hole thermodynamics, but also they lead to the expected Smarr formula for the WAdS$_{3}$ black holes. We also show that the black hole's entropy obeys the Cardy formula of the dual conformal field theory (CFT).