A K3 sigma model with ℤ2 8: Double-struck M sign20 symmetry

Abstract

The K3 sigma model based on the Z2-orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra suˆ(2)6. By combining these different viewpoints we show that the N = (4, 4) preserving symmetries of this theory are described by the discrete symmetry group Z82 : M20. This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.