Rational conformal field theories with G2 holonomy -: art. no. 008

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.