Superconformal field theories for compact G2 manifolds -: art. no. 006

We present the construction of exactly solvable superconformal field theories describing type-II string models compactified on compact G(2) manifolds. These models are defined by anti-holomorphic quotients of the form (CY x S-1)/Z(2), where we realize the Calabi-Yau as a Gepner model. In the superconformal field theory the Z(2) acts as charge conjugation implying that the representation theory of a W(2; 4; 6; 8; 10) algebra plays an important role in the construction of these models. Intriguingly, in all three examples we study, including the quintic, the massless spectrum in the Z(2) twisted sector of the superconformal field theory differs from what one expects from the supergravity computation. This discrepancy is explained by the presence of a discrete NS-NS background two-form flux in the Gepner model.