Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and Spin(7) Holonomy

TL;DR

This paper explores flux configurations in type II string theory compactifications, their dual brane descriptions, and introduces new geometric structures with G(2) and Spin(7) holonomy related to supersymmetry preservation.

Contribution

It proposes a geometric description of fluxes via G(2) and Spin(7) holonomy manifolds, including a novel Spin(7) manifold not fitting known classes, linked to supersymmetry levels.

Findings

Fluxes described by G(2) holonomy metrics in M-theory.

Existence of a new Spin(7) holonomy manifold for 1/4 supersymmetry.

Dual brane web configurations for flux setups.

Abstract

We discuss fluxes of RR and NSNS background fields in type II string compactifications on non-compact Calabi-Yau threefolds together with their dual brane description which involves bound states of branes. Simultaneously turning on RR and NSNS 2-form fluxes in an 1/2 supersymmetric way can be geometrically described in M-theory by a SL(2,Z) family of metrics of G(2) holonomy. On the other hand, if the flux configuration only preserves 1/4 of supersymmetries, we postulate the existence of a new eight-dimensional manifold with spin(7) holonomy, which does not seem to fit into the classes of known examples. The latter situation is dual to a 1/4 supersymmetric web of branes on the deformed conifold. In addition to the 2-form fluxes, we also present some considerations on type IIA NSNS 4-form and 6-form fluxes.