Root-TT̄ deformations on causal self-dual electrodynamic theories

A bstract 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, ℓ ( 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 ∂ ℓ ∂ τ ≥ 1 and ∂² ∂ τ²≥ 0 ∂ 2 ℓ ∂ τ 2 ≥ 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 T T ¯ operator. Additionally, we derive marginal and irrelevant flow equations for the logarithmic causal self-dual electrodynamics.