Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules

TL;DR

This paper links meromorphic Jacobi forms of half-integral index to umbral moonshine, constructing vertex operator superalgebras to realize these forms and exploring their connection to mock modular forms.

Contribution

It introduces a new association between meromorphic Jacobi forms and umbral moonshine, solving the module problem for four cases through explicit algebraic constructions.

Findings

Constructed vertex operator superalgebras for four umbral moonshine cases.

Established a relationship between meromorphic Jacobi forms and mock modular forms.

Provided a general framework for meromorphic Jacobi forms of half-integral index.

Abstract

In this work we consider an association of meromorphic Jacobi forms of half-integral index to the pure D-type cases of umbral moonshine, and solve the module problem for four of these cases by constructing vertex operator superalgebras that realise the corresponding meromorphic Jacobi forms as graded traces. We also present a general discussion of meromorphic Jacobi forms with half-integral index and their relationship to mock modular forms.