Duality Symmetric Actions

TL;DR

This paper develops a method to construct duality-symmetric actions for theories with antisymmetric tensor fields, allowing global symmetries to be realized at the action level, with applications to string theory compactifications.

Contribution

It introduces a general procedure for formulating duality-symmetric actions that incorporate both potentials, enabling symmetries of field equations to be realized as symmetries of the action.

Findings

SL(2,R) symmetry can be realized in the action similar to O(6,22) duality.

The method allows global symmetries to be elevated to action symmetries.

SL(2,Z) symmetry may naturally emerge in a dual formulation of heterotic string theory.

Abstract

It is frequently useful to construct dual descriptions of theories containing antisymmetric tensor fields by introducing a new potential whose curl gives the dual field strength, thereby interchanging field equations with Bianchi identities. We describe a general procedure for constructing actions containing both potentials at the same time, such that the dual relationship of the field strengths arises as an equation of motion. The price for doing this is the sacrifice of manifest Lorentz invariance or general coordinate invariance, though both symmetries can be realized nonetheless. There are various examples of global symmetries that have been realized as symmetries of field equations but not actions. These can be elevated to symmetries of the action by our method. The main example that we focus on is the low-energy effective action description of the heterotic string theory compactified on a six-torus to four dimensions. We show that the SL(2,R) symmetry, whose SL(2,Z) subgroup has been conjectured to be an exact symmetry of the full string theory, can be realized on the action in a way that brings out a remarkable similarity to the target space duality symmetry O(6,22). Our analysis indicates that SL(2,Z) symmetry may arise naturally in a dual formulation of the theory.