Symmetries of K3 sigma models

It is shown that the supersymmetry-preserving automorphismsof any non-linear $\sigma$-model on K3 generate a subgroupof the Conway group Co$_1$. This is the stringygeneralization of the classical theorem, due to Mukai andKondo, showing that the symplectic automorphisms of any K3manifold form a subgroup of the Mathieu group $\MM_{23}$.The Conway group Co$_1$ contains the Mathieu group$\MM_{24}$ (and therefore in particular $\MM_{23}$) as asubgroup. We confirm the predictions of the Theorem withthree explicit conformal field theory (CFT) realizations of K3: the ${\mathbbT}^4/\ZZ_2$ orbifold at a self-dual point, and the twoGepner models $(2)^4$ and $(1)^6$. In each case wedemonstrate that their symmetries do not form a subgroup of$\MM_{24}$, but lie inside Co$_1$ as predicted by ourTheorem.

Full Text (PDF format)

Published 12 July 2012