Higher-derivative Gravitation in Bosonic and Superstring Theories and a New Mechanism for Supersymmetry Breaking

A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of auxiliary fields. As a by-product we present a consistent non-linear coupling of a spin-2 tensor to gravitation. It is shown that non-vanishing (Cμναβ) 2 terms arise in N = 1, D = 4 superstring Lagrangians due to one-loop radiative corrections with light field internal lines. We discuss the general form of quadratic (1, 1) supergravity in two dimensions, and show that this theory is equivalent to two scalar supermultiplets coupled to the usual Einstein supergravity. It is demonstrated that the theory possesses stable vacua with vanishing cosmological constant which spontaneously break supersymmetry. 1. Bosonic Gravitation The usual Einstein theory of gravitation involves a symmetric tensor gμν whose dynamics is determined by the Lagrangian