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

TL;DR

This work extends the AdS/CFT correspondence to the ${\cal N}=1$ quiver theory arising from D3-branes at the conifold, identifying wrapped D3-branes on a $S^3$ inside $T^{1,1}$ with baryon-like operators and showing their dimensions satisfy $\Delta=3N/4$, in agreement with the IR dimensions of the bifundamental fields. It furthermore analyzes D5-brane domain walls on the $S^2$ of $T^{1,1}$, demonstrating a gauge-group transition ${SU(N)\times SU(N)}\rightarrow {SU(N)\times SU(N+1)}$ across the wall and explaining the accompanying string-creation dynamics. These results provide concrete holographic realizations of baryons and domain walls in a non-${\bf S}^5$ background and offer a pathway to supergravity duals of more general ${\cal N}=1$ ${SU(N_1)\times SU(N_2)}$ theories, strengthening AdS/CFT's reach beyond the maximally supersymmetric case. The study also connects finite-$N$ phenomena to quantum mechanics on curved spaces via Landau-level degeneracies, reinforcing the consistency of the duality.

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.