Massless Flavor in Geometry and Matrix Models

TL;DR

This paper investigates the inclusion of massless and massive flavor fields in N=1 gauge theories using geometric engineering and matrix models, reconciling previous debates and reproducing field theory results.

Contribution

It provides a geometric framework for treating massless and massive flavors equally in matrix models and superpotentials, clarifying their role in gauge theories.

Findings

Reproduces field theory superpotentials from geometric transitions.

Treats massless and massive flavors on equal footing.

Provides insights via T-dual brane constructions.

Abstract

The proper inclusion of flavor in the Dijkgraaf-Vafa proposal for the solution of N=1 gauge theories through matrix models has been subject of debate in the recent literature. We here reexamine this issue by geometrically engineering fundamental matter with type IIB branes wrapped on non-compact cycles in the resolved geometry, and following them through the geometric transition. Our approach treats massive and massless flavor fields on equal footing, including the mesons. We also study the geometric transitions and superpotentials for finite mass of the adjoint field. All superpotentials we compute reproduce the field theory results. Crucial insights come from T-dual brane constructions in type IIA.