Abstract

We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H 4 (BG, Z). In a similar way, possible Wess-Zumino in-teractions of such a group G are classified by H 3 (G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H 4 (BG, Z) to H 3 (G, Z). We generalize this correspon-dence to topological ‘spin ’ theories, which are defined on three manifolds with spin structure, and are related to what might be called Z2 graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the for-mulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.

Citations