Baryons and Domain Walls in an N = 1 Superconformal Gauge Theory

TL;DR

This paper explores the correspondence between wrapped D-branes in string theory on a conifold and baryon-like operators in an N=1 superconformal gauge theory, revealing insights into domain walls and gauge group transitions.

Contribution

It identifies baryon-like operators with wrapped D3-branes and studies domain walls via D5-branes, proposing duals for different gauge group configurations.

Findings

Matching of operator dimensions between supergravity and field theory

Identification of domain walls changing gauge groups

Proposal of supergravity duals for varied gauge theories

Abstract

Coincident D3-branes placed at a conical singularity are related to string theory on $AdS_5\times X_5$, for a suitable five-dimensional Einstein manifold $X_5$. For the example of the conifold, which leads to $X_5=T^{1,1}=(SU(2)\times SU(2))/U(1)$, the infrared limit of the theory on $N$ D3-branes was constructed recently. This is ${\cal N}=1$ supersymmetric $SU(N)\times SU(N)$ gauge theory coupled to four bifundamental chiral superfields and supplemented by a quartic superpotential which becomes marginal in the infrared. In this paper we consider D3-branes wrapped over the 3-cycles of $T^{1,1}$ and identify them with baryon-like chiral operators built out of products of $N$ chiral superfields. The supergravity calculation of the dimensions of such operators agrees with field theory. We also study the D5-brane wrapped over a 2-cycle of $T^{1,1}$, which acts as a domain wall in $AdS_5$. We argue that upon crossing it the gauge group changes to $SU(N)\times SU(N+1)$. This suggests a construction of supergravity duals of ${\cal N}=1$ supersymmetric $SU(N_1)\times SU(N_2)$ gauge theories.