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

TL;DR

This paper constructs supersymmetric five brane solutions on the resolved cone over Y^{p,q} spaces, providing a framework for studying back-reacted branes in complex geometries relevant to string theory.

Contribution

It introduces explicit supersymmetric five brane solutions on the resolved cone over Y^{p,q} and develops a framework for analyzing back-reacted branes in these geometries.

Findings

Existence of supersymmetric five branes wrapped on two-cycles.

Development of an Ansatz and equations of motion for back-reacted solutions.

Construction of explicit solutions and asymptotic expansions.

Abstract

Motivated by recent developments in the understanding of the connection between five branes on resolved geometries and the corresponding generalizations of complex deformations in the context of the warped resolved deformed conifold, we consider the construction of five branes solutions on the resolved cone over Y^{p,q} spaces. We establish the existence of supersymmetric five 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 the construction of fully back-reacted five branes; we present an Ansatz and the corresponding equations of motion. Our results establish a detailed framework to study back-reacted five branes wrapped on the resolved cone over Y^{p,q} and as a first step we find explicit solutions and construct an asymptotic expansion with the expected properties.