Off-Shell Duality in Born-Infeld Theory

TL;DR

This paper explores the implementation of SL(2,Z) duality in Maxwell and Born-Infeld theories, demonstrating modular invariance of the action and partition function, and addressing complexification of fields in Born-Infeld theory.

Contribution

It introduces a novel approach to realize SL(2,Z) duality as linear non-local transformations on potentials in these theories.

Findings

The action and partition function are modular invariant in any gauge.

SL(2,Z) duality can be implemented as linear non-local transformations.

Longitudinal fields in Born-Infeld theory must be complexified.

Abstract

The classical equations of motion of Maxwell and Born-Infeld theories are known to be invariant under a duality symmetry acting on the field strengths. We implement the SL(2,Z) duality in these theories as linear but non-local transformations on the potentials. We show that the action and the partition function in the Hamiltonian formalism are modular invariant in any gauge. For the Born-Infeld theory we find that the longitudinal part of the fields have to be complexified.