SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions
Differential Geometry
2015-04-13 v4 High Energy Physics - Theory
Number Theory
Abstract
We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta functions and harmonic Maass forms. We also derive further such generating functions for the SO(3)-Donaldson invariants with 2N_f massless monopoles using the geometry of certain rational elliptic surfaces (N_f=0,2,3,4). We show that the partition function for N_f=4 is nearly modular. When combined with one of Ramanujan's mock theta functions, we obtain a weight 1/2 modular form. This fact is central to the proof of the conjecture.
Keywords
Cite
@article{arxiv.0808.1442,
title = {SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions},
author = {Andreas Malmendier and Ken Ono},
journal= {arXiv preprint arXiv:0808.1442},
year = {2015}
}
Comments
56 pages, accepted for publication In Geometry and Topology