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

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.