SL(2,R) Invariance of Non-Linear Electrodynamics Coupled to An Axion and a Dilaton

TL;DR

This paper develops an $SL(2, ext{R})$ invariant framework for non-linear electrodynamics coupled with an axion and dilaton, identifying a unique generalization of Born-Infeld theory with such symmetry.

Contribution

It introduces a general $SL(2, ext{R})$ invariant Lagrangian for non-linear electrodynamics coupled to axion and dilaton fields, including a unique extension of Born-Infeld theory.

Findings

Derived $SL(2, ext{R})$ invariant equations of motion.

Identified a unique $SL(2, ext{R})$ invariant Born-Infeld generalization.

Formulated a comprehensive Lagrangian framework for coupled fields.

Abstract

The most general Lagrangian for non-linear electrodynamics coupled to an axion $a$ and a dilaton $\phi$ with $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion is $$ -\half\left(\nabla\phi\right)^2 - \half e^{2\phi}\left(\nabla a\right)^2 + \fraction{1}{4}aF_{\mu\nu}\star F^{\mu\nu} + L_{\rm inv}(g_{\mu\nu},e^{-\frac{1}{2}\phi}F_{\rho\sigma}) $$ where $L_{\rm inv}(g_{\mu\nu},F_{\rho\sigma})$ 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 $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion.