Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models

TL;DR

This paper investigates gravitational corrections in supersymmetric gauge theories with flavors using matrix models, deriving formulas and connecting results to conformal field theory and topological string theory.

Contribution

It provides a compact formula for annulus contributions and relates the full R^2 correction to a CFT correlator, advancing understanding of gravitational effects in gauge theories.

Findings

Derived a formula for the annulus contribution using the prime form.

Reproduced the R^2 correction via a CFT correlator.

Confirmed the N=2 limit matches instanton and topological A-model results.

Abstract

We study the gravitational corrections to the F-term in four-dimensional N=1 U(N) gauge theories with flavors, using the Dijkgraaf-Vafa theory. We derive a compact formula for the annulus contribution in terms of the prime form on the matrix model curve. Remarkably, the full R^2 correction can be reproduced as a special momentum sector of a single c=1 CFT correlator, which closely resembles that in the bosonization of fermions on Riemann surfaces. The N=2 limit of the torus contribution agrees with the multi-instanton calculations as well as the topological A-model result. The planar contributions, on the other hand, have no counterpart in the topological gauge theories, and we speculate about the origin of these terms.