M-theory Conifolds

TL;DR

This paper introduces a new family of G_2 holonomy metrics D_7 in seven-manifolds, exploring their relation to conifold transitions and mirror symmetry in M-theory, with implications for topology change.

Contribution

It derives first-order equations for D_7 metrics with S^3×S^3 orbits, linking them to resolved conifolds and expanding understanding of G_2 manifolds in M-theory.

Findings

D_7 metrics relate to resolved conifold at weak coupling

They exhibit asymptotically locally conical geometry

Parameter controls S^3 bolt squashing and topology transition

Abstract

Seven-manifolds of G_2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G_2 metrics D_7, with S^3\times S^3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B_7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D_7 metrics' non-trivial parameter characterises the squashing of an S^3 bolt, which limits to S^2 at weak coupling. In general the D_7 metrics are asymptotically locally conical, with a nowhere-singular circle action.