Abstract
We investigate the \( T\overline{T} \)-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 \( T\overline{T} \) operator from a simple integration technique. We show that this flow equation is compatible with \( T\overline{T} \) 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 \( T\overline{T} \) 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 \( T\overline{T} \) 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 \( T\overline{T} \) operator and quadratic form of the energy-momentum tensor in D = 4.
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Babaei-Aghbolagh, H., Velni, K.B., Yekta, D.M. et al. \( T\overline{T} \)-like flows in non-linear electrodynamic theories and S-duality. J. High Energ. Phys. 2021, 187 (2021). https://doi.org/10.1007/JHEP04(2021)187
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DOI: https://doi.org/10.1007/JHEP04(2021)187