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

TL;DR

This paper links flux configurations in Type II string theory to explicit M-theory geometries by showing that 1/2 BPS RR+NSNS 2-form fluxes lift to $G_2$-holonomy manifolds in M-theory, while certain 1/4 BPS fluxes necessitate novel eight-dimensional Spin(7) backgrounds dual to 1/4-BPS brane webs on the deformed conifold. It interprets fluxes through torus fibrations, maps them to dual brane constructions (D6-KK bound states, $(N,N')$ 5-brane webs), and analyzes how T- and S-dualities organize the flux data into $SL(2,\mathbb{Z})$ multiplets. The work also extends to higher-form fluxes (4- and 6-forms), clarifying their roles in the four- and three-dimensional superpotentials and their M-theory origins via $G^{(4)}$, $H^{(7)}$, and related structures. Together, these results illuminate how non-perturbative effects in low-dimensional supersymmetric theories arise from geometric and brane configurations in M-theory, with Spin(7) backgrounds providing a geometric realization of 1/4-BPS fluxes and brane webs.

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.