Duality Symmetries in Non-Linear Gauge Theories

TL;DR

This paper investigates duality symmetries in non-linear gauge theories involving antisymmetric tensor fields, establishing conditions for compact duality groups and exploring extensions to non-compact groups via scalar field couplings.

Contribution

It derives conditions on Lagrangians for duality symmetry in non-linear gauge theories and provides examples of duality-invariant models, extending the symmetry groups through scalar field couplings.

Findings

Duality symmetry groups are compact when no scalar fields are present.

Conditions on Lagrangians for duality invariance are established.

Extensions to non-compact duality groups via scalar fields are discussed.

Abstract

Duality symmetries are discussed for non-linear gauge theories of (n-1)-th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be compact. We find conditions on the Lagrangian required by compact duality symmetries and show an example of duality invariant non-linear theories. We also discuss how to enlarge the duality symmetries to non-compact groups by coupling scalar fields described by non-linear sigma models.