LOCALLY SUPERSYMMETRIC D=3 NONLINEAR SIGMA-MODELS

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N = 1 and 2 the target space of these models is riemannian or Kahler, respectively. All N > 2 theories are associated with Einstein spaces. For N = 3 the target space is quaternionic, while for N = 4 it generally decomposes into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N = 5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N = 9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F4(-20), E6(-14), E7(-5) and E8(+8), respectively. For N = 3 and N greater-than-or-equal-to 5 the D = 2 theories obtained by dimensional reduction are two-loop finite.