We investigate the $$ T\overline{T} $$ T T ¯ -like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$ T T ¯ operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$ T T ¯ deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$ T T ¯ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$ T T ¯ operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$ N = 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$ T T ¯ operator and quadratic form of the energy-momentum tensor in D = 4.

Recently, 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.

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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.

Recently it has been speculated that the S-matrix elements on the world volume of D 3 -branes should satisfy the Ward identity corresponding to the S-duality transformations. For a single brane and in the low energy limit, this indicates that in the Abelian Dirac-Born-Infeld and Chern-Simons actions, the combination of contact terms and tree-level massless poles in an n-point function should satisfy the S-duality. In this paper, we examine in details the S-matrix element of three gauge bosons and one 2-form and the S-matrix element of six gauge bosons in favor of the above proposal.

In this paper, we will investigate a manifestly SL(2, R)-invariant structure for the energy-momentum tensor of ModMax theory as a nonlinear modification of Maxwell electrodynamics which includes conformal invariance as well. In the context of this theory, we show that the energy-momentum tensor of the generalized Born-Infeld theory can also be written in the same invariant form. We will find manifestly duality-invariant parts of the actions corresponding to the invariant couplings λ and γ in these theories. It can be shown that the resultant actions correspond to the irrelevant and marginal $$ T\overline{T} $$ T T ¯ -like deformations, respectively.

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