The Gravitational Path Integral and Critical Dimensions of Linear and Nonlinear Locally Supersymmetric σ Models

Abstract

It is well known that Slavnov-Taylor identities can be derived from path integrals by making a change of integration variable which corresponds to a symmetry transformation and using the fact that the classical action is invariant under this symmetry. When the measure is invariant under the symmetry transformation one obtains only contributions from the action and external sources. For rigid symmetries, one first replaces the parameter by a local parameter and in this way the Noether current enters in the Ward identities. For local symmetries with external gauge fields one can make a local classical gauge transformation, but if the gauge fields are dynamical, one must instead consider the rigid BRST symmetry of the quantum action.