Representations of the Mapping Class Group of the Two Punctured Torus on the Space of \hat {sl}(2,C) Spin1/2-Spin1/2 Kac-Moody Blocks

TL;DR

This paper constructs an infinite class of representations of the mapping class group of the two punctured torus using integral representations of $ ext{sl}(2, ext{C}) $ Kac-Moody blocks, linking free field methods to topological group actions.

Contribution

It introduces a novel approach to represent the mapping class group via integral representations derived from free field realizations.

Findings

Derived an infinite class of mapping class group representations

Connected free field representations to topological group actions

Extended understanding of $ ext{sl}(2, ext{C}) $ Kac-Moody algebra representations

Abstract

The integral representations of the $\hat {sl}(2,C)$ Spin 1/2 - Spin 1/2 Kac-Moody Blocks on the torus, arising from the free field representation of the $\hat {sl}(2,C)$ Kac-Moody algebra of Wakimoto and Bernard and Felder, are used to derive an infinite class of representations of the mapping class group of the two punctured torus.