T-dualising the Deformed and Resolved Conifold

TL;DR

This paper extends T-duality techniques to construct explicit 1/4-BPS solutions involving NS5-branes on resolved and deformed conifolds, revealing geometric parameters as brane separation and deformation moduli.

Contribution

It refines the formalism for T-duality to generate new solutions on resolved and deformed conifolds, linking geometric parameters to brane configurations.

Findings

Constructed solutions for NS5-branes on resolved and deformed conifolds.

Mapped conifold parameters to brane separation and deformation.

Provided explicit solutions to sourced Monge--Ampere equations.

Abstract

In a previous paper we used T-duality to construct a new type of 1/4-BPS solution describing a pair of NS5-branes intersecting in 1+3 dimensions and localised in all other directions except for a single transverse circle. This led to an explicit solution to a sourced Monge--Ampere equation, of which there are few known examples. In this paper we refine this formalism and apply it to two important generalisations: the resolved and deformed conifolds. In doing so we construct two new solutions describing, respectively, a pair of NS5-branes separated in a transverse direction and a pair of NS5-branes with smooth `diamond' profile. We show how the parameter of the resolved conifold (size of the S^2) maps to a transverse separation of the NS5-branes, while the modulus of the deformed conifold (size of the S^3) maps to the deformation parameter of the diamond web.