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Motivated by recent developments in the understanding of the connectionbetween five branes on resolved geometries and the correspondinggeneralizations of complex deformations in the context of the warped resolveddeformed conifold, we consider the construction of five branes solutions on theresolved cone over Y^{p,q} spaces. We establish the existence of supersymmetricfive branes solutions wrapped on two-cycles of the resolved cone over Y^{p,q}in the probe limit. We then use calibration techniques to begin theconstruction of fully back-reacted five branes; we present an Ansatz and thecorresponding equations of motion. Our results establish a detailed frameworkto study back-reacted five branes wrapped on the resolved cone over Y^{p,q} andas a first step we find explicit solutions and construct an asymptoticexpansion with the expected properties.

Toward NS5 Branes on the Resolved Cone over Y^{p,q}