$T\bar{T}$-like Flows in Non-linear Electrodynamic Theories and S-duality

TL;DR

This paper explores $Tar{T}$-like deformations in non-linear electrodynamics across various dimensions, revealing compatibility with certain theories, differences from AdS/CFT-based deformations, and preservation of symmetries like $SL(2,R)$.

Contribution

It introduces a new approach to $Tar{T}$ deformations in higher-dimensional non-linear electrodynamics, highlighting their unique features and symmetry properties.

Findings

Compatibility with $Tar{T}$ deformation in 2D scalar theories.

Distinct nature of higher-dimensional $Tar{T}$ flows from AdS/CFT expectations.

Preservation of $SL(2,R)$ symmetry in Born-Infeld theories.

Abstract

We investigate the $T\bar{T}$-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 $T\bar{T}$ operator from a simple integration technique. We show that this flow equation is compatible with $T\bar{T}$ 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 $T\bar{T}$ 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 $T\bar{T}$ operator preserves the original $SL(2,R)$ symmetry of a non-supersymmetric Born-Infeld theory, as well as $\mathcal{N}=2$ supersymmetric model. It is shown that the corresponding $SL(2,R)$ invariant action fixes the relationship between the $T\bar{T}$ operator and quadratic form of the energy-momentum tensor in $D\!=\!4$.