Local gauge and Lorentz invariance of the heterotic string theory

Abstract

The Hull-Witten proof of the local gauge and Lorentz invariance of the σ-model describing the propagation of the heterotic string in arbitrary background field is extended to higher orders in α'. The modification of the transformation laws of the antisymmetric tensor field under these symmetries is discussed. Finally we point out the existence of an anomally in the naive N=½ supersymmetry transformation, and show that is is cancelled by the same counterterms which restore local Lorentz and gauge invariance of the σ-model.