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arXiv · 1803.09270

An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on $\mathbb{P}^2$

Kathrin Bringmann·Caner Nazaroglu
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Abstract

Topologically twisted $\mathcal{N} = 4$ super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold $\mathbb{P}^2$ and with gauge group $\mathrm{U}(3)$ this partition function has a holomorphic anomaly which makes it a mock modular form of depth two. We employ the Circle Method to find a Rademacher expansion for the Fourier coefficients of this partition function. This is the first example of the use of Circle Method for a mock modular form of a higher depth.

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Kathrin Bringmann, Caner Nazaroglu. 2018-03-25. An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on $\mathbb{P}^2$. https://arxiv.org/abs/1803.09270

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