We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane ℂℙ2. We experimentally study the growth of the coefficients for gauge group SU(2) and SU(3), which are examples of mock modular forms of depth 1 and 2 respectively. We also introduce the notion of ``mock cusp form'', and study an example of weight 3 related to the SU(3) partition function. Numerical experiments on the first 200 coefficients suggest that the coefficients of a mock modular form of weight k grow as the coefficients of a modular form of weight k, that is to say as nk−1. On the other hand the coefficients of the mock cusp form appear to grow as n3/2, which exceeds the growth of classical cusp forms of weight 3. We provide bounds using saddle point analysis, which however largely exceed the experimental observation.
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Meeting ID: 880 9276 6911
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