Rational Conformal Field Theories With G_2 Holonomy

TL;DR

This paper constructs rational conformal field theories for strings on seven-dimensional G_2 holonomy manifolds, proposing models based on Z_2 orbifolds of N=2 theories, and explores their geometric and D-brane implications.

Contribution

It introduces a novel approach to building rational CFTs for G_2 manifolds using Z_2 orbifolds of N=2 models, extending Gepner model techniques.

Findings

No new Ramond ground states unless all levels are even

Classical orbifold singularities cannot be resolved without breaking G_2 holonomy

Discussion of supersymmetric boundary states and D-branes in these models

Abstract

We study conformal field theories for strings propagating on compact, seven-dimensional manifolds with G_2 holonomy. In particular, we describe the construction of rational examples of such models. We argue that analogues of Gepner models are to be constructed based not on N=1 minimal models, but on Z_2 orbifolds of N=2 models. In Z_2 orbifolds of Gepner models times a circle, it turns out that unless all levels are even, there are no new Ramond ground states from twisted sectors. In examples such as the quintic Calabi-Yau, this reflects the fact that the classical geometric orbifold singularity can not be resolved without violating G_2 holonomy. We also comment on supersymmetric boundary states in such theories, which correspond to D-branes wrapping supersymmetric cycles in the geometry.