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 ${\mathrm{AdS}}_5\times X_5,$ for a suitable five-dimensional Einstein manifold $X_5.$ For the example of the conifold, which leads to $X_5{=T}^{1,1}=\left[\mathrm{SU}\right(2)\mathrm{}\times \mathrm{SU}(2\left)\mathrm{}\right]/U\left(1\right),$ the infrared limit of the theory on N D3-branes was constructed recently. This is an N=1 supersymmetric $\mathrm{SU}\left(N\right)\mathrm{}\times \mathrm{SU}\left(N\right)\mathrm{}$ 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 ${\mathrm{AdS}}_5.$ We argue that upon crossing it the gauge group changes to $\mathrm{SU}\left(N\right)\mathrm{}\times \mathrm{SU}(N+1\mathrm{}).$ This suggests a construction of supergravity duals of N=1 supersymmetric ${SU(N}_1)\times {SU(N}_2)$ gauge theories.