An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on $\mathbb{P}^2$
Number Theory
2018-09-25 v2 High Energy Physics - Theory
Algebraic Geometry
Abstract
Topologically twisted super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold and with gauge group 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.
Cite
@article{arxiv.1803.09270,
title = {An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on $\mathbb{P}^2$},
author = {Kathrin Bringmann and Caner Nazaroglu},
journal= {arXiv preprint arXiv:1803.09270},
year = {2018}
}
Comments
23 pages; v2: 25 pages, the discussion of asymptotic expansion extended, to appear in Transactions of the AMS