Connections, field redefinitions and heterotic supergravity

Abstract

We study heterotic supergravity at O(α′), first described in detail in 1989 byBergshoeff and de Roo. In particular, we discuss the ambiguity of a connection choice onthe tangent bundle. It is well known that in order to have a consistent supergravity withsupersymmetry transformations given in the usual way, this connection must be the Hullconnection at O(α′). We consider deformations of this connection corresponding to fieldredefinitions, and the necessary corrections to the supersymmetry transformations. Wealso discuss possible extensions of this theory to higher orders in α′. We are interested inthe moduli space of such field redefinitions which allow for supersymmetric solutions to theequations of motion. We show that for solutions on M4×X, where M4 is Minkowski and Xis compact, this is given by H(0,1)(X,End(TX)). This space corresponds to infinitesimallyclose connections for which the equations of motion are satisfied. The setup suggestsa symmetry between the gauge connection and the tangent bundle connection, as alsoemployed by Bergshoeff and de Roo. We propose that this symmetry should be kept toconnection used in curvature computations.