3-branes on resolved conifold

TL;DR

The paper constructs and analyzes Type IIB backgrounds with D3-branes on the resolved conifold, including fractional branes, by two complementary approaches: (i) deriving the explicit Ricci-flat Kahler metric on the resolved conifold and solving the D3-brane equations with constant dilaton and self-dual fluxes, and (ii) generalizing the conifold ansatz asymmetrically to obtain a one-dimensional radial action that admits a superpotential and reduces to a first-order system. It presents the explicit resolved conifold metric, exhibits D3-brane and fractional D3-brane solutions, and examines their UV and IR behavior, finding a UV match to the conifold case but an IR repulson-type singularity with possible enhançon-type resolution. A unifying feature is the existence of a simple, shared superpotential structure that yields first-order equations, applicable to both the resolved and deformed conifold geometries, thereby linking the three classical conifold backgrounds through a common supersymmetric framework. These results broaden the landscape of gauge/gravity duals for N=1 theories and provide a robust tool for exploring radial (RG-like) flows in compactified geometries with fluxes.

Abstract

The type IIB supergravity solution describing a collection of regular and fractional D3 branes on the conifold (hep-th/0002159) was recently generalized to the case of the deformed conifold (hep-th/0007191). Here we present another generalization -- when the conifold is replaced by the resolved conifold. This solution can be found in two different ways: (i) by first explicitly constructing the Ricci-flat Kahler metric on resolved conifold and then solving the supergravity equations for the D3-brane ansatz with constant dilaton and (self-dual) 3-form fluxes; (ii) by generalizing the ``conifold'' ansatz of hep-th/0002159 in a natural ``asymmetric'' way so that the 1-d action describing radial evolution still admits a superpotential and then solving the resulting 1-st order system. The superpotentials for the ``resolved'' and ``deformed'' conifold cases turn out to have essentially the same simple structure. The solution in the resolved conifold case has the same asymptotic UV behaviour as in the conifold case, but unlike the deformed conifold case is still singular in the IR. The naked singularity is of repulson type and may have a brane resolution.