Decompositions of index one Jacobi forms into $N=4$ characters and formulas for mock modular forms

TL;DR

This paper demonstrates that all weak Jacobi forms of weight zero and index one can be decomposed into N=4 superconformal characters, providing explicit formulas for related mock modular forms and their completions.

Contribution

It introduces a decomposition of Jacobi forms into N=4 characters and derives explicit formulas for associated mock modular forms and their universal completions.

Findings

Decomposition of Jacobi forms into N=4 superconformal characters.

Explicit formulas for mock modular forms and their completions.

Application to Jacobi trace functions in super vertex operator algebras.

Abstract

It is shown that every weak Jacobi form of weight zero and index one on a congruence subgroup of the full Jacobi group can be decomposed into $N=4$ superconformal characters. Additionally, a simple expression for the mock modular form determining the superconformal character coefficients is obtained, as well as a universal completion structure. Along the way, a useful vector-valued mock modular form is also found and studied. These results are applied to analyze some Jacobi trace functions associated to super vertex operator algebras and a distinguished sector.