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

2021/03/08 by Krauel, Matthew, Mason, Geoffrey, Tuite, Michael +1
#FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2103.04561

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.

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• Jacobi Forms of Critical Weight and Weil Representations
• Mock modular forms whose shadows are Eisenstein series of integral weight
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• Modified Jacobi forms of index zero
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