Mock theta functions and characters of N=3 superconformal modules II

TL;DR

This paper derives explicit formulas for certain mock theta functions related to N=3 superconformal modules and applies these to compute characters and supercharacters of these modules, advancing understanding in mathematical physics.

Contribution

It provides explicit formulas for mock theta functions when parameters are half-integers and applies these to characterize N=3 superconformal modules.

Findings

Explicit formulas for $\

Character and supercharacter formulas for N=3 modules.

Abstract

We obtain an explicit formula for the mock theta function $\Phi^{[m,s]}$ in the case when either $m$ or $s$ is a half of an odd integer by using the coroot lattice of $D(2,1;a)$. This enables us, together with the recurrence formula for $\Phi^{[m,s]}$, to know $\Phi^{[m,s]}$ for all $m$ and $s$. As its application, we deduce explicit formulas for the character and the supercharacter of N=3 modules obtained from the quantum Hamiltonian reduction of $\hat{osp}(3|2)$-modules.