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

Abstract

We investigate the 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 T operator from a simple integration technique. We show that this flow equation is compatible with T T deformation of nonlinear Born-Infeld type theories in D = 2 and D = 4 dimensions. However, our computation discloses that this kind of T T flow is in conflict with the deformation of Born-Infeld theory in D ≥ 6. As an illustrative investigation in 4D, we find that our construction for the T T operator preserves the original SL(2, R) symmetry of a non-supersymmetric Born-Infeld theory, as well as N = 2 supersymmetric model. It is shown that the corresponding SL(2, R) invariant action fixes the relationship between the T T operator and quadratic form of energy-momentum tensor in 4D.

Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations

“…To do this, we will first find the EMT and then using operator (1.4) deform the ModMax theory from simple integration technique proposed in ref. [32]. It is shown that the emergent deformed theory is the GBI theory given in ref.…”

“…Following the prescription in [32], we are going to find the interacting terms for the ModMax lagrangian (1.3) from a T T perturbative approach. The resulting deformed theory would not respect the conformal symmetry, however carry some symmetry such as SL(2, R), because the EMT preserves this symmetry.…”

“…A T T operator in 2D CFT is an irrelevant operator given by the product of T = T zz and T = T zz components of the EMT. One may also consider a generalization to higher-dimensional QFTs with a higher-dimensional version of T T operator [28][29][30][31][32]. It has been found in refs.…”

“…For instance, in ref. [32] we have studied the construction of T T deformation for some NED BI-type theories in general (2n)-dimensional spacetime as follows…”

“…In this regard, we identified the tension of D 3 -brane, on which the low energy effective action lives, with the deformation parameter λ as T 3 = 1/(2πα ′ ) 2 = λ −1 . Due to usage of the EMT in NED theories to reconstruct the deformed action by operator (1.4), it is expected that the symmetries of EMT, as electromagnetic duality, be inherited to O λ T 2 [32]. (see e.g., [15] for SL(2, R) invariant form of EMT for NED.)…”