Causal self-dual nonlinear electrodynamics from the Born-Infeld theory

Abstract

Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{\hat{I}¼\hat{I}½};g)$, where $F_{\hat{I}¼\hat{I}½}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(\ddot{I}ˆ)$. Our formulation is based on the Lagrangian $\mathfrak{L}(F_{\hat{I}¼\hat{I}½};\ddot{I}ˆ)=L(F_{\hat{I}¼\hat{I}½};\ddot{I}ˆ)+W(\ddot{I}ˆ)$, where $\ddot{I}ˆ$ is an auxiliary scalar field. Integrating out $\ddot{I}ˆ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(\ddot{I}ˆ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend.

14 pages; V2: comments and references added