On conformal field theories at fractional levels

For each lattice one can define a free boson theory propagating on the corresponding torus. We give an alternative definition where one employs any automorphism of the group $M^{\ast }\mathrm{/}M$. This gives a wealth of conformal data, which we realize as some bosonic theory, in all the `regular’ cases. We discuss the generalization to affine theories. As a byproduct, we compute the gauss sum for any lattice and any diagonal automorphism.