Root-TT̄ Deformations on Causal Self-Dual Electrodynamic Theories

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, $τ$, and Courant-Hilbert functions, (τ), which depend on $τ$. Recent studies have shown that duality-invariant nonlinear electromagnetic theories fulfill the principle of causality under the conditions ∂ /∂ τ ≥ 1 and ∂² /∂ τ² ≥ 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-TT̄ operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics and identify a symmetry referred to as $α$-symmetry, which is present in all these models.