Gauging of Nonlinearly Realized Symmetries

TL;DR

This paper explores the relationship between nonlinear and linear realizations of symmetries in gauge theories, revealing a geometric interpretation of BRST charges and applying it to superstring theory equivalence.

Contribution

It demonstrates that BRST charges for nonlinear and linear realizations are related via a geometric similarity transformation, with applications to superstring theory.

Findings

BRST charges are related by a similarity transformation.

The transformation has a geometric interpretation as an exterior derivative.

Application to superstring theory shows equivalence with bosonic string theory.

Abstract

A representation of a subgroup H of a finite-dimensional group G can be used to induce a nonlinear realization of G. If the nonlinearly realized symmetry is gauged, then the BRST charge can be related by a similarity transformation to the BRST charge for the gauged linear realization of H (plus a cohomologically trivial piece). It is shown that the relation between the two BRST charges is a reflection of the fact that they can be interpreted geometrically as expressions for the exterior derivative on G relative to two different bases, and an explicit expression for the generator of the similarity transformation is obtained. This result is applied in an infinite-dimensional setting, where it yields the similarity transformation used by Ishikawa and Kato to prove the equivalence of the Berkovits-Vafa superstring with the underlying bosonic string theory.