Symmetries of K3 sigma models

Abstract

It is shown that the supersymmetry-preserving automorphisms of any non-linear sigma-model on K3 generate a subgroup of the Conway group Co_1. This is the stringy generalisation 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_{23}. The Conway group Co_1 contains the Mathieu group M_{24} (and therefore in particular M_{23}) as a subgroup. We confirm the predictions of the Theorem with three explicit CFT realisations of K3: the T^4/Z_2 orbifold at the 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_{24}, but lie inside Co_1 as predicted by our Theorem.

40 pages

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Cited by in corpus (5)

• Fricke S-duality in CHL models
• On symmetries of N=(4,4) sigma models on T^4
• K3 String Theory, Lattices and Moonshine
• Mathieu Moonshine and Orbifold K3s
• Mathieu Moonshine and symmetries of K3 sigma models