The theory of new minimal supergravity and its matter couplings in heterotic string theory

There are four different supergravity theories in d = 4 space-time. We develop a method of deformations of stress tensors in string theory and, using this method, show that only new minimal supergravity theory is obtained from heterotic string. We also work out the couplings of matter linear multiplet to new minimal supergravity. We give a method of deforming the stress tensors for the bosonic and fermionic string corresponding to turning on the target space background fields and describe a procedure for obtaining the transformations of the background fields under a target space symmetry group. After illustrating these methods with examples, we apply them to the case of the chiral superfields which arise when the six internal dimensions of the fermionic string are compactified into a $Z\sb3$-orbifold and obtain the N = 1 supersymmetry transformations of the chiral superfields. We then apply this method of deformations of the stress energy tensor to the case of the heterotic sting compactified to d = 4 space-time preserving N = 1 supersymmetry. We construct a new vertex operator associated with an auxiliary antisymmetric background field in the supergravity sector and show that the construction is unique. We, then, obtain the supersymmetry transformations of the background fields and find them to be the same as those of the component fields of the new minimal supergravity multiplet and a physical linear multiplet coupled to new minimal supergravity. We also show that it is not possible to construct a vertex operator associated with an auxiliary scalar supergravity background field. We conclude that the heterotic string gives new minimal supergravity for any arbitrary compactification to four dimensional space-time preserving N = 1 supersymmetry. We also construct matter action in new minimal supergravity. We present the most general coupling of a linear supermultiplet to new minimal supergravity, modified by the addition of the Chern-Simons term associated with the auxiliary field gauge connection, both in superfields and component fields. We show that Chern-Simons term induces, through the Bianchi identities, a kinetic energy term for this gauge connection and a propagating spin 1/2 superpartner. Furthermore, the induced vector supermultiplet acquires a non-vanishing mass