T T ¯ $$ T\overline{T} $$ -like flows in non-linear electrodynamic theories and S-duality

• Main Authors: H. Babaei-Aghbolagh, Komeil Babaei Velni, Davood Mahdavian Yekta, H. Mohammadzadeh
• Format: Article
• Language: English
• Published: SpringerOpen 2021-04-01
• Series: Journal of High Energy Physics
• Subjects: Field Theories in Higher Dimensions; Duality in Gauge Field Theories; Supersymmetry and Duality; Effective Field Theories
• Online Access: https://doi.org/10.1007/JHEP04(2021)187

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