Comments on the N=1 SU(M+p)xSU(p) quiver gauge theory with flavor

TL;DR

This paper analyzes the supersymmetric vacua of a complex N=1 cascading gauge theory with flavor, exploring its Coulomb and Higgs branches through both field theory and string theory perspectives, including quantum corrections.

Contribution

It provides a detailed study of the Higgs branch, including quantum corrections and instanton effects, linking field theory results with D7-brane geometry in the bulk.

Findings

Higgs branch includes non-perturbative instanton effects.

Quantum corrections modify the classical moduli space.

Field theory and bulk computations of operator VEVs agree.

Abstract

We study supersymmetric vacua of the N=1 cascading SU(M+p)xSU(p) gauge theory with flavor - the theory on p D3-branes and M wrapped D5-branes at the tip of the conifold, and N_f flavor D7-branes wrapping a holomorphic four-cycle inside the conifold. The Coulomb branch of the moduli space is inherited from the pure gauge theory without flavor and was thoroughly studied in the past. Besides, there is a Higgs branch where some D3 and/or D5-branes dissolve in the D7-branes forming the worldvolume gauge instantons. We study the Higgs branch both from the field theory and the bulk point of view. On the classical level the moduli space is closely related to the one of the N=2 C^2/Z_2 orbifold theory, in particular certain vacua of the N=1 theory are related to noncommutative instantons on the resolved C^2/Z_2. On the quantum level the Higgs branch acquires corrections due to renormalization of the Kahler potential and non-perturbative effects in field theory. In the bulk this is encoded in the classical D7-brane geometry. We compute the VEVs of the protected operators and the field theory RG flow and find an agreement with the parallel computations in the bulk.