Localisation of the Third Way Theory

TL;DR

This thesis explores supersymmetric localisation techniques applied to the Third Way Theory, a deformation of topologically massive Yang-Mills in three dimensions, providing new supersymmetrisation and non-perturbative analysis methods.

Contribution

It introduces a supersymmetrisation of the Third Way Theory and develops localisation methods to derive non-perturbative results for this theory.

Findings

Supersymmetrisation of the Third Way Theory achieved

Localization method applied to derive non-perturbative results

Analysis of supersymmetric systems in one and three dimensions

Abstract

The following is a master thesis centered around the concept of localisation and the Third Way Theory. This thesis discusses various aspects of supersymmetric localisation in one and three dimensions, and contains original results with regards to the Third Way Theory. It starts off with the Witten index for a one-dimensional supersymmetric system and derives various aspects through localisation. After this, the thesis moves on to the Third Way Theory. First, it offers a review of the Third Way Theory, a deformation of topologically massive Yang-Mills theory in three dimensions. Then it moves on to original results. These include a supersymmetrisation of the Third Way Theory and consequently a localisation of the Third Way Theory, which is to say, a method of deriving non-perturbative results.