Holomorphicity and Modularity in Seiberg-Witten Theories with Matter

TL;DR

This paper computes gravitational corrections in N=2 SU(2) Seiberg-Witten theories with matter, utilizing modularity and holomorphic anomaly equations, and compares results with matrix model approaches.

Contribution

It introduces a method to determine gravitational corrections using modularity and boundary conditions, extending previous pure gauge results to theories with matter.

Findings

Gravitational corrections are fixed by the gap condition at dyon singularities.

Behavior of corrections at conformal points is analyzed.

Results are consistent with matrix model loop equations.

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.