NEW SUPERGRAVITIES WITH CENTRAL CHARGES AND KILLING SPINORS IN 2-DIMENSIONS(1)

We construct a new class of (p,q)-extended Poincare supergravity theor ies in 2+1 dimensions as Chern-Simons theories of supersymmetry algebr as with both central and automorphism charges. The new theories have t he advantage that they are limits of corresponding (p,q) adS supergrav ity theories and, for not too large a value of N = p + q, that they ha ve a natural formulation in terms of off-shell superfields, in which c ontext the distinction between theories having the same value of N but different (p,q) arises because of inequivalent conformal compensator superfields. We also show that, unlike previously constructed N-extend ed Poincare supergravity theories, the new (2,0) theory admits conical spacetimes with Killing spinors. Many of our results on (2,0) Poincar e supergravity continue to apply in the presence of coupling to N = 2 supersymmetric sigma-model matter.