Curved space resolution of the singularity of fractional D3-branes on a conifold

We construct a supergravity dual to the cascading SU(N+M)×SU(N) supersymmetric gauge theory (related to fractional D3-branes on a conifold according to Klebanov and co-workers) in the case when the three-space is compactified on S³ and in the phase with unbroken chiral symmetry. The size of S³ serves as an infrared cutoff on the gauge-theory dynamics. For a sufficiently large S³ the dual supergravity background is expected to be nonsingular. We demonstrate that this is indeed the case: we find a smooth type IIB supergravity solution using a perturbation theory that is valid when the radius of S³ is large. We consider also the case with the Euclidean world volume being S⁴ instead of R×S³, where the supergravity solution is again found to be regular. This ``curved space'' resolution of the singularity of the fractional D3-branes on the conifold solution is analogous to the one in the nonextremal (finite temperature) case discussed in our previous work.