Rational Conformal Field Theories With G 2 Holonomy

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.