SO(2,C) Invariant Discrete Gauge States in Liouville Gravity Coupled to Minimal Conformal Matter

TL;DR

This paper derives a general formula for discrete gauge states in Liouville gravity coupled to minimal conformal matter, revealing an SO(2,C) invariant structure analogous to BRST cohomology.

Contribution

It provides a unified formula for discrete gauge states in c<1 Liouville theory and demonstrates their SO(2,C) invariance, extending previous results at c=1.

Findings

Derived a general formula for DGS in c<1 Liouville theory

Reproduced known c=1 DGS in the appropriate limit

Showed SO(2,C) invariance of DGS in covariant quantization

Abstract

We contruct 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.