M-theory on `toric' G_2 cones and its type II reduction

TL;DR

This paper constructs explicit G_2 metrics with symmetries, derives their type II string theory reductions, and confirms their interpretation as brane configurations, generalizing previous models in M-theory and string theory.

Contribution

It provides explicit G_2 metrics with symmetries, their IIA and IIB reductions, and detailed brane interpretations, extending recent theoretical models.

Findings

Explicit G_2 metrics with two isometries derived.

Type IIA and IIB backgrounds obtained from M-theory reductions.

Confirmed interpretation as localized IIA 6-branes and delocalized IIB 5-branes.

Abstract

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extract the IIA reduction of M-theory on such backgrounds, as well as its type IIB dual. By studying the asymptotics of type II fields around the relevant loci, we confirm the interpretation of such backgrounds in terms of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS forms in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.