SO(2,C) invariant discrete gauge states in liouville gravity coupled to minimal conformal matter

Abstract

We construct the general formula for a set of discrete gauge states (DGS) in c < 1 Liouville theory. This formula reproduces the previously found c = 1 DGS in the appropriate limiting case. We also demonstrate the SO(2,C) invariant structure of these DGS in the old covariant quantization of the theory. This is in analogy to the SO(2,C) invariant ring structure of BRST cohomology of the theory.