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

TL;DR

This paper constructs a smooth supergravity dual for a cascading gauge theory on curved space, resolving the singularity of fractional D3-branes on the conifold by compactifying space on S^3 or S^4, demonstrating regular solutions in these cases.

Contribution

It provides the first explicit supergravity solutions for fractional D3-branes on conifold with curved space compactification, resolving singularities via a large S^3 or S^4.

Findings

Supergravity solutions are smooth for large S^3 radius.

Regular solutions are also found with S^4 compactification.

Curved space resolution parallels finite temperature case.

Abstract

We construct a supergravity dual to the cascading $SU(N+M) x SU(N)$ 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 $R x S^3$, 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.