A Note on Seiberg Duality for $N_{f} < N_{c}$

TL;DR

This paper explores Seiberg duality in supersymmetric QCD with fewer flavors than colors, using string theory brane configurations to propose and support a dual magnetic theory with specific gauge group and matter content.

Contribution

It introduces a brane-based construction for Seiberg duality in the case of $N_f < N_c$, including a detailed analysis of the IR superpotential and dual gauge theory.

Findings

Proposes a brane configuration realizing the magnetic dual for $N_f < N_c$.

Shows the IR theory matches the Affleck-Dine-Seiberg superpotential.

Supports the duality using anomaly matching and M-theory lift.

Abstract

We consider SQCD for $N_{f}<N_{c}$. We use a brane configuration in type IIA string theory to propose a Seiberg dual. The brane configuration that realises the magnetic theory contains $N_{f}$ branes and $N_{c}-N_{f}$ \textit{anti}-branes, leading to an $SU(N_{c}-N_{f})$ gauge theory with $N_{f}$ flavours. The potential between the branes triggers a RG flow and we argue that the IR theory realises the Affleck-Dine-Seiberg superpotential. We use both field theory arguments, in particular anomaly matching, and a lift of the type IIA brane configuration to M-theory, in order to support our proposal.