Steps towards Lattice Virasoro Algebras: su(1,1)

TL;DR

This paper constructs an explicit su(1,1) subalgebra action on path spaces for minimal models, demonstrating how it determines the Virasoro algebra's central charge and relating it to Temperley-Lieb algebra generators.

Contribution

It provides a new explicit construction of the su(1,1) subalgebra action on path spaces and links it to the Virasoro algebra and Temperley-Lieb algebra representations.

Findings

Fixes the central charge for the Lee-Yang edge singularity

Constructs a representation using Temperley-Lieb algebra generators

Advances understanding of lattice Virasoro algebra structures

Abstract

An explicit construction is presented for the action of the su(1,1) subalgebra of the Virasoro algebra on path spaces for the c(2,q) minimal models. In the case of the Lee-Yang edge singularity, we show how this action already fixes the central charge of the full Virasoro algebra. For this case, we additionally construct a representation in terms of generators of the corresponding Temperley-Lieb algebra.