Marginal TTˉT\bar{T}-Like Deformation and ModMax Theories in Two Dimensions

Recently, the ModMax theory has been proposed as a unique conformal nonlinear extension of electrodynamics. We have shown in [1] that this modification can be reproduced a marginal $T\bar{T}$-like deformation from pure Maxwell theory. Further, this deformation is solved by using a perturbative approach. In this letter, we will investigate another ModMax-like deformation for a two-dimensional (2D) scalar field theory. In this regard, we first find a marginal $T\bar{T}$-like deformation in two dimensions and then reproduce the MM-like Lagrangian from a multiple 2D scalar field theory.Comment: 11 pages, improved versio

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

The relationship between thermodynamics and the Lloyd bound on the holographic complexity for a black hole has been of interest. We consider $D$ dimensional anti-de Sitter black holes with hyperbolic geometry as well as black holes with momentum relaxation that have a minimum for temperature and mass. We 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 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 behaviour of action complexity and thermodynamic curvature at minimum temperature, we propose the action complexity as an order parameter of the black holes as thermodynamic systems. Also, we derive the critical exponent related to the thermodynamic curvature in different dimensions.Comment: 14 pages, 10 figure

On SL(2,R) symmetry in nonlinear electrodynamics theories

AbstractRecently, it has been observed that the Noether–Gaillard–Zumino (NGZ) identity holds order by order in α′ expansion in nonlinear electrodynamics theories as Born–Infeld (BI) and Bossard–Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the SL(2,R) duality in all orders of α′ expansion in the Einstein frame. In this paper we show that there are the SL(2,R) invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These SL(2,R) invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of α′ expansion. The SL(2,R) symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of SL(2,R) invariant structures

Complexity growth in Gubser–Rocha models with momentum relaxation

The Einstein–Maxwell–Axion–Dilaton (EMAD) theories, based on the Gubser–Rocha (GR) model, are very interesting in holographic calculations of strongly correlated systems in condensed matter physics. Due to the presence of spatially dependent massless axionic scalar fields, the momentum is relaxed, and we have no translational invariance at finite charge density. It would be of interest to study some aspects of quantum information theory for such systems in the context of AdS/CFT where EMAD theory is a holographic dual theory. For instance, in this paper we investigate the complexity and its time dependence for charged AdS black holes of EMAD theories in diverse dimensions via the complexity equals action (CA) conjecture. We will show that the growth rate of the holographic complexity violates Lloyd’s bound at finite times. However, as shown at late times, it depends on the strength of the momentum relaxation and saturates the bound for these black holes