On conformal field theories at fractional levels Original Research Article

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∗/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.