On SL(2;R) symmetry in nonlinear electrodynamics theories

TL;DR

This paper demonstrates that $SL(2,R)$ symmetry is preserved in the energy-momentum tensors of nonlinear electrodynamics theories like Born-Infeld and Bossard-Nicolai, across all orders of $\alpha'$ expansion, especially when coupled with an axion.

Contribution

It establishes the $SL(2,R)$ invariance of energy-momentum tensors in axion-coupled nonlinear electrodynamics theories at all orders of $\alpha'$ expansion.

Findings

$SL(2,R)$ invariance in energy-momentum tensors is shown for BI and BN theories.

$SL(2,R)$ symmetry appears as a multiplication of Maxwell Lagrangian and invariant structures.

Invariant structures persist at all orders of $\alpha'$ expansion.

Abstract

Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in $\alpha'$ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the $SL(2,R)$ duality in all orders of $\alpha'$ expansion in the Einstein frame. In this paper we show that there are the $SL(2,R)$ invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These $SL(2,R)$ invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of $\alpha'$ expansion. The $SL(2,R)$ symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of $SL(2,R)$ invariant structures.