Fusion Rules in Logarithmic Superconformal Minimal Models

Abstract

Logarithmic conformal field theory is a relatively recent branch of mathematical physics which gives rise to interesting representations of symmetry algebras through the process of fusion. Fusion is fundamental to the study of conformal field theories and mathematically may be considered to be something of an abstract tensor product of representations. This has been made more precise through an algorithmic approach developed by Nahm, Gaberdiel and Kausch and coded by several research groups. Such an algorithm has been implemented for the case of Virasoro algebra but not in the super-symmetric case. In this thesis we delve into the details of modifying and applying the NGK algorithm for the N=1 super Virasoro algebra and study the representations that arise in both the Neveu-Schwarz and Ramond sector. The algorithm has been encoded in the SAGE programming environment.