Root-$T\bar{T}$ Deformations on Causal Self-Dual Electrodynamic Theories

Abstract

The self-dual condition, which ensures invariance under electromagnetic duality, manifests as a partial differential equation in nonlinear electromagnetism theories. The general solution to this equation is expressed in terms of an auxiliary field, $\tau$, and Courant-Hilbert functions, $\ell (\tau )$, which depend on $\tau$. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions $\frac{\partial \ell }{\partial \tau }\ge 1$ and $\frac{{\partial }^2\ell }{\partial {\tau }^2}\ge 0$. In this paper, we investigate theories with two coupling constants that also comply with the principle of causality. We demonstrate that these theories possess a new universal representation of the root-$T\bar{T}$ operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics and identify a symmetry referred to as $\alpha$-symmetry, which is present in all these models.

arXiv comment17 pages, no figures, Refined version to match JHEP published