Extended Holomorphic Anomaly in Gauge Theory

Details Extended Holomorphic Anomaly in Gauge Theory Extended Holomorphic Anomaly in Gauge Theory

2010-07-01

arxiv.org/abs/1007.0263v1

Lett.Math.Phys.95:67-88,2011

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1007/s11005-010-0432-2

The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special geometry. Modularity together with the (beta-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the orbifold radius, corresponding to beta=2, can be identified with an "orientifold" of the theory at beta=1. The various connections give hints for embedding the structure into the topological string.

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