Modular Invariants of $N=2$ Supersymmetric $SU(1,1)$ Models

TL;DR

This paper investigates the modular invariance properties of N=2 superconformal SU(1,1) models by decomposing characters of a Kazama-Suzuki model to construct modular invariant partition functions.

Contribution

It introduces a novel decomposition of Kazama-Suzuki characters to explicitly construct modular invariant partition functions for SU(1,1) models.

Findings

Successfully decomposed Kazama-Suzuki characters into simpler components.

Constructed explicit modular invariant partition functions.

Enhanced understanding of modular properties in N=2 superconformal models.

Abstract

We study the modular invariance of $N=2$ superconformal $SU(1,1)$ models. By decomposing the characters of Kazama-Suzuki model $SU(3)/(SU(2)\times U(1))$ into an infinite sum of the characters of $(SU(1,1)/U(1))\times U(1)$ we construct modular invariant partition functions of $(SU(1,1)/U(1))\times U(1)$.