SL(2, [formula omitted]) invariance of non-linear electrodynamics coupled to an axion and a dilaton

Abstract

The most general Lagrangian for non-linear electrodynamics coupled to an axion a and a dilaton φ with SL(2, R ) invariant equations of motion is − 1 2 (∇φ) 2 − 1 2 e 2φ (∇a) 2 + 1 4 aF μν ★ F μν + L inv (g μν, e − 1 2 φ F ϱσ) where L inv( g μν , F ϱσ ) is a Lagrangian whose equations of motion are invariant under electric-magnetic duality rotations. In particular there is a unique generalization of Born-Infeld theory admitting SL(2, R ) invariant equations of motion.