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

Abstract

We construct a supergravity dual to the cascading $SU(N+M)xSU(N)$ supersymmetric gauge theory (related to fractional D3-branes on conifold according to Klebanov et al) in the case when the 3-space is compactified on $S^3$ and in the phase with unbroken chiral symmetry. The size of $S^3$ serves as an infrared cutoff on the gauge theory dynamics. For a sufficiently large $S^3$ 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 $S^3$ is large. We consider also the case with the euclidean world-volume being $S^4$ instead of $Rx{S}^3$, where the supergravity solution is again found to be regular. This ``curved space'' resolution of the singularity of the fractional D3-branes on conifold solution is analogous to the one in the non-extremal (finite temperature) case discussed in our previous work.

25 pages, latex

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