Holomorphic Anomaly in Gauge Theories and Matrix Models

Details Holomorphic Anomaly in Gauge Theories and Matrix Models Holomorphic Anomaly in Gauge Theories and Matrix Models

2006-05-19

arxiv.org/abs/hep-th/0605195v2

JHEP0709:054,2007

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 2 eps figures, expansion at the monopole point corrected and interpreted, and references added

Scientific paper

10.1088/1126-6708/2007/09/054

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold. In both cases we construct propagators that give a recursive solution in the genus modulo a holomorphic ambiguity. In the case of Seiberg-Witten theory the gravitational corrections can be expressed in closed form as quasimodular functions of Gamma(2). In the matrix model we fix the holomorphic ambiguity up to genus two. The latter result establishes the Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the matrix model at fixed genus in closed form in terms of generalized hypergeometric functions.

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