ALEPH(0)-EXTENDED SUPERGRAVITY AND CHERN-SIMONS THEORIES

We give generalizations of extended Poincare supergravity with arbitra rily many supersymmetries in the absence of central charges in three d imensions by gauging its intrinsic global SO(N) symmetry. We call thes e N-0 (Aleph-null) supergravity theories. We further couple a non-Abel ian supersymmetric Chem-Simons theory and an Abelian topological BF th eory to N-0 supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chem-Simons theories beyond N = 4. This fe ature is peculiar to the Chem-Simons and BF theories including supergr avity in three dimensions. We also show that dimensional reduction sch emes for four-dimensional theories such as N = 1 self-dual supersymmet ric Yang-Mills theory or N = 1 supergravity theory that can generate N -0 globally and locally supersymmetric theories in three dimensions. A s an interesting application, we present N-0 supergravity Liouville th eory in two dimensions after appropriate dimensional reduction from th ree dimensions.