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

TL;DR

This paper derives explicit formulas for certain mock theta functions related to N=3 superconformal modules using Lie superalgebra techniques and applies these to analyze tensor product branching functions, confirming a previous conjecture.

Contribution

It provides explicit formulas for mock theta functions associated with N=3 modules and proves a conjectured branching function formula.

Findings

Explicit formulas for mock theta functions $\

Verification of the conjectured branching function formula

Abstract

In this paper we obtain explicit formulas for mock theta functions $\Phi^{[m,s]}(\tau, z_1, z_2,t)$ $(m \in \frac12 \mathbf{N}, s \in \frac12 \mathbf{Z})$ by using the coroot lattice of the Lie superalgebra $D(2,1,a)$ and the Kac-Peterson's identity. As its application, we study the branching functions of tensor products of N=3 modules and prove the formula conjectured in the previous paper.