Symmetries of K3 sigma models

Abstract

It is shown that the supersymmetry-preserving automorphisms of any non-linear σ-model on K3 generate a subgroup of the Conway group Co1. This is the stringy generalization of the classical theorem, due to Mukai and Kondo, showing that the symplectic automorphisms of any K3 manifold form a subgroup of the Mathieu group M{doublestruck}23. The Conway group Co1 contains the Mathieu group M{doublestruck}24 (and therefore in particular M{doublestruck}23) as a subgroup. We confirm the predictions of the Theorem with three explicit conformal field theory (CFT) realizations of K3: the T4/Z2 orbifold at a self-dual point, and the two Gepner models (2)4 and (1)6. In each case we demonstrate that their symmetries do not form a subgroup of M{doublestruck}24, but lie inside Co1 as predicted by our Theorem.