Hyperkähler isometries of K3 surfaces

Abstract

Abstract We consider symmetries of K3 manifolds. Holomorphic symplectic automorphisms of K3 surfaces have been classified, and observed to be subgroups of the Mathieu group M 23. More recently, automorphisms of K3 sigma models commuting with SU(2) × SU(2) R-symmetry have been classified by Gaberdiel, Hohenegger, and Volpato. These groups are all subgroups of the Conway group. We fill in a small gap in the literature and classify the possible hyperkähler isometry groups of K3 manifolds. There is an explicit list of 40 possible groups, all of which are realized in the moduli space. The groups are all subgroups of M 23.

Keywords

• Discrete Symmetries
• Extended Supersymmetry
• Gauge Symmetry
• String Duality