Holomorphic D7-Branes and Flavored N=1 Gauge Theories

TL;DR

The paper develops a holographic description of flavored N=1 gauge theories by embedding holomorphic D7-branes in the conifold, yielding a dual field theory with fundamental quarks and a superpotential that couples them to the bifundamental matter. In the probe limit and its leading backreaction, the author constructs a supersymmetric gravity solution that encodes a Seiberg duality cascade and shows how the presence of flavors slows the cascade. The flavor contributions modify the radial running so that the effective color ranks decrease by M per duality step and by K due to flavors, potentially stopping in the IR and yielding small gauge groups. The work connects to a Type IIA brane picture under T-duality and sets the stage for future studies of chiral symmetry breaking, meson spectra, and F-theory completions of warped, flavored backgrounds.

Abstract

We consider D7-branes in the gauge theory/string theory correspondence, using a probe approximation. The D7-branes have four directions embedded holomorphically in a non-compact Calabi-Yau 3-fold (which for specificity we take to be the conifold) and their remaining four directions are parallel to a stack of D3-branes transverse to the Calabi-Yau space. The dual gauge theory, which has $\mathcal{N}=1$ supersymmetry, contains quarks which transform in the fundamental representation of the gauge group, and we identify the interactions of these quarks in terms of a superpotential. By activating three-form fluxes in the gravity background, we obtain a dual gauge theory with a cascade of Seiberg dualities. We find a supersymmetric supergravity solution for the leading backreaction effects of the D7-branes, valid for asymptotically large radius. The cascading theory with flavors exhibits the interesting phenomenon that the rate of the cascade slows and can stop as the theory flows to the infrared.