Holomorphicity and Modularity in Seiberg-Witten Theories with Matter

Understand

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.