Generalisations of the Russo-Townsend formulation

Abstract

As a generalisation of the recent construction by Russo and Townsend, we propose a new approach to generate $\mathsf{U}(1)$ duality-invariant models for nonlinear electrodynamics. It is based on the use of two building blocks: (i) a fixed (but otherwise arbitrary) model for self-dual nonlinear electrodynamics with Lagrangian $L(F_{\hat{I}¼\hat{I}½};g)$ depending on a duality-invariant parameter $g$; and (ii) an arbitrary potential $W(\ddot{I}ˆ)$, with $\ddot{I}ˆ$ an auxiliary scalar field. It turns out that the model $\mathfrak{L}(F_{\hat{I}¼\hat{I}½};\ddot{I}ˆ)=L(F_{\hat{I}¼\hat{I}½};\ddot{I}ˆ)+W(\ddot{I}ˆ)$ leads to a self-dual theory for nonlinear electrodynamics upon elimination of $\ddot{I}ˆ$. As an illustration, we work out two examples in which the seed Lagrangian $L(F_{\hat{I}¼\hat{I}½};g)$ corresponds to the Born-Infeld model and two particular potentials $W(\ddot{I}ˆ)$ are chosen such that integrating out $\ddot{I}ˆ$ gives: (i) the ModMaxBorn theory; and (ii) the ModMax theory. We also briefly discuss supersymmetric generalisations of the proposed formulation.

13 pages; V4: Reference and new example (ModMax from Born-Infeld) added