Rolling among G_2 vacua

TL;DR

This paper explores topology-changing transitions between G_2 manifolds derived from CY threefolds, classifies involutions, and discusses implications for effective theories and mirror candidates.

Contribution

It classifies antiholomorphic involutions on CY threefolds without fixed points and relates conifold transitions to G_2 manifold topology changes, including fixed point cases.

Findings

Conifold transitions induce topology changes in G_2 manifolds.

Examples of G_2 manifolds with identical Betti sum are provided.

Transition mechanisms relate to scalar potential and Higgs phenomena.

Abstract

We consider topology-changing transitions between 7-manifolds of holonomy G_2 constructed as a quotient of CY x S^1 by an antiholomorphic involution. We classify involutions for Complete Intersection CY threefolds, focussing primarily on cases without fixed points. The ordinary conifold transition between CY threefolds descends to a transition between G_2 manifolds, corresponding in the N=1 effective theory incorporating the light black hole states either to a change of branch in the scalar potential or to a Higgs mechanism. A simple example of conifold transition with a fixed nodal point is also discussed. As a spin-off, we obtain examples of G_2 manifolds with the same value for the sum of Betti numbers b_2+b_3, and hence potential candidates for mirror manifolds.