Ring of physical states in the M(2,3) Minimal Liouville gravity

TL;DR

This paper develops a recursive method to construct BRST cohomology classes in M(2,3) Minimal Liouville gravity, revealing the algebraic structure of physical states through explicit singular vectors.

Contribution

It introduces a novel recursive construction for BRST cohomology in M(2,3) Minimal Liouville gravity using explicit singular vectors, and establishes the operator algebra of physical states.

Findings

Recursive construction of BRST cohomology classes

Explicit form of singular vectors in Virasoro modules

Operator algebra of physical states

Abstract

We consider the M(2,3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We construct an algebra of operators acting on the BRST cohomology space. The operator algebra of physical states is established by use of these operators.