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Consistency of Orbifold Conformal Field Theories on K3
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We explicitly determine the locations of G orbifold conformal field theories, G=Z_M, M=2,3,4,6, G=\hat D_n, n=4,5, or G the binary tetrahedral group \hat T, within the moduli space M^{K3} of N=(4,4) superconformal field theories associated to K3. This is achieved purely from the known description of the moduli space [AM94] and the requirement of a consistent embedding of orbifold conformal field theories within M^{K3}. We calculate the Kummer type lattices for all these orbifold limits. Our method allows an elementary derivation of the B-field values in direction of the exceptional divisors that arise from the orbifold procedure [Asp95,Dou97,BI97], without recourse to D-geometry. We show that our consistency requirement fixes these values uniquely and determine them explicitly. The relation of our results to the classical McKay correspondence is discussed.
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Tracking the symmetries of $\mathbb Z_3$-orbifold K3s within the Mathieu groups
The holomorphic symplectic automorphism group of a Z3-orbifold K3 is (Z3)^2 ⋊ Z4, realized inside M12 and M24, and it combines with Kummer symmetries to generate M24.
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