CHERN-SIMONS THEORIES WITH SUPERSYMMETRIES IN 3 DIMENSIONS

We study various Chem-Simons (CS) theories in three dimensions with extended supersymmetries. Starting with remarks on nonsupersymmetric cases, we give (i) N = 2 non-Abelian CS theories, (ii) N = 4 non-Abelian CS theory, (iii) conformal supergravity CS theories for general N greater-than-or-equal-to 2 up to N = infinity, (iv) CS action in terms of composite gauge fields, based on the N = 1 supersymmetric SO(n + 1)/SO(n) sigma model, (v) relationship of CS theories with higher-dimensional supersymmetric theories, especially with ten-dimensional heterotic string theory, (vi) a prototype model yielding the N = 2 CS theories, (vii) N = 8M and N = 8M - 2 extended supersymmetric Abelian CS theories, and (viii) CS theories for graded Lie groups. Some remarks on anyon models and supersymmetric Jones polynomials are also given.