Higher-Rank Supersymmetric Models and Topological Field Theory

TL;DR

This paper explores higher-rank supersymmetric models extending N=2 minimal models, identifies key operator structures, and constructs associated topological conformal field theories with novel features.

Contribution

It introduces a new class of topological field theories derived from higher-rank supersymmetric models, distinct from traditional N=2 minimal model twistings.

Findings

Identification of chirality conditions and chiral ring analogs

Construction of topological conformal field theories from higher-rank models

Demonstration of BRST-exactness and analysis of physical observables

Abstract

In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$ minimal model. In particular we identify the analogs of chirality conditions and chiral ring. In the second part we construct a class of topological conformal field theories starting with this higher-rank supersymmetric model. We show the BRST-exactness of the twisted stress-energy tensor, find out physical observables and discuss how to make their correlation functions. It is emphasized that in the case of $su(2)$ the topological field theory constructed in this paper is distinct from the one obtained by twisting the $N=2$ minimal model through the usual procedure.