Duality-symmetric Action for Electromagnetic Theory with Electric and Magnetic Sources

TL;DR

This paper develops a duality-symmetric action for electromagnetism with electric and magnetic sources, incorporating SL(2,R) invariance, and extends it to Born-Infeld theory relevant for string theory D-branes.

Contribution

It formulates a local, duality-symmetric action using two potentials for SL(2,R) invariance, including quantum and string theory applications.

Findings

Constructed a duality-symmetric action with two potentials

Extended the framework to SL(2,Z) invariance in quantum theory

Presented a Born-Infeld version relevant for D-brane physics

Abstract

For the SL(2,\textbf{R}) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials $A^\mu$ and $B^\mu$ in a judicious way. On the two potentials $A^\mu$ and $B^\mu$ the SL(2,\textbf{R}) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,\textbf{Z})-invariant action. Also given is a Zwanziger-type action for SL(2,\textbf{R}) duality-invariant Born-Infeld electrodynamics which can be important for D-brane dynamics in string theory.