LORENTZ AND U(1) CHERN-SIMONS TERMS IN NEW MINIMAL SUPERGRAVITY

We couple a linear multiplet to new minimal supergravity, modified by the addition of both the U (1) and Lorentz superfield Chern-Simons terms. We write the lagrangian in component form and find that it contains pieces quadratic in the curvature tensor and has only a finite number of terms. We also find the auxiliary fields a(m) and approximately G(m) become propagating and massive. Very interestingly, however, for a particular ratio of the U (1) and Lorentz Chern-Simons terms, approximately G(m) can be eliminated. This leads to a lagrangian with only a finite number of terms containing a propagating, massive vector field a(m) and terms quadratic in the curvature tensor.