2018/10/16 by Korpas, Georgios
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1810.07057
We revisit the u-plane integral of the topologically twisted N=2 super Yang-Mills theory, the Donaldson-Witten theory, on a closed four-manifold X with embedded surfaces that support supersymmetric surface operators. This integral mathematically corresponds to the generating function of the ramified Donaldson invariants of X. By including a Q-exact deformation to the u-plane integral we are able to re-express its integrand in terms of a total derivative with respect to an indefinite theta function, a special kind of mock modular form. We show that for specific Kähler surfaces of Kodaira dimension -∞ the integral localizes at the cusp at infinity of the Coulomb branch of the theory.