A K3 sigma model with Z_2^8:M_{20} symmetry

Understand

The K3 sigma model based on the Z_2-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 su(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 Z_2^8:M_{20}.
• This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models.