Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry

TL;DR

This paper explores how non-Kahler metrics on resolved conifolds can restore supersymmetry in supergravity solutions with wrapped D5-branes, linking flux configurations to geometric torsion constraints and M-theory fluxes.

Contribution

It constructs explicit non-Kahler metrics satisfying torsion constraints and analyzes their M-theory duals with localized G-fluxes, advancing understanding of supersymmetry restoration.

Findings

Explicit non-Kahler metrics satisfying torsion constraints

Identification of localized G-fluxes as harmonic two-forms

Relations between flux configurations and geometric constraints

Abstract

The known supergravity solution for wrapped D5-branes on the two-cycle of a Kahler resolved conifold is in general ISD but not supersymmetric, with the supersymmetry being broken by the presence of (1, 2) fluxes. However if we allow a non-Kahler metric on the resolved conifold, supersymmetry can easily be restored. The vanishing of the (1, 2) fluxes here corresponds to, under certain conformal rescalings of the metric, the torsion class constraints. We construct a class of explicit non-Kahler metrics on the resolved conifold satisfying the constraints. All this can also be studied from M-theory, where the fluxes and branes become non-localized G-fluxes on deformed Taub-NUT spaces. Interestingly, the gauge fluctuations on the wrapped D5-branes appear now as localized G-fluxes in M-theory. These localized fluxes are related to certain harmonic two-forms that are normalizable. We compute these forms explicitly and discuss how new constraints on the geometry of the non-Kahler manifolds may appear from M-theory considerations.