Holomorphicity and Modularity in Seiberg-Witten Theories with Matter

Abstract

We calculate the gravitational corrections to the effective action of N=2 SU(2) Seiberg-Witten theory with matter using modularity, the holomorphic anomaly equation and expected behavior at the boundaries of the moduli space. As in pure gauge theory we show that the gap condition at the dyon singularities completely fixes the gravitational corrections. We discuss the behavior of the gravitational corrections at the conformal points. We compare our results with the recursive solution of the loop equation in the matrix model approach, which provides in addition open amplitudes.

53 pages, no figures

References in corpus (17)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Open string amplitudes and large order behavior in topological string theory
• Remodeling the B-model
• Direct Integration of the Topological String
• Integrability of the holomorphic anomaly equations
• Holomorphic anomaly and matrix models
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• A holomorphic and background independent partition function for matrix models and topological strings
• Multi-Instantons and Multi-Cuts
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Seiberg-Witten theory and matrix models
• Polynomial Structure of the (Open) Topological String Partition Function
• Global Properties of Topological String Amplitudes and Orbifold Invariants
• Topological open strings on orbifolds
• All orders asymptotic expansion of large partitions
• Topological Strings and (Almost) Modular Forms
• The Real Topological String on a local Calabi-Yau

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