A K3 sigma model with Z_2^8:M_{20} symmetry

Abstract

The K3 sigma model based on the Z_2-orbifold of the D_4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra su(2)^6. By combining these different viewpoints we show that the N=(4,4) preserving symmetries of this theory are described by the discrete symmetry group Z_2^8:M_{20}. This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.

55 pages

References in corpus (8)

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Cited by in corpus (18)

• Fricke S-duality in CHL models
• N=4 Superconformal Bootstrap of the K3 CFT
• On symmetries of N=(4,4) sigma models on T^4
• Quantum stabilizer codes, lattices, and CFTs
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Supersymmetry and the Suzuki chain
• $\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$
• Dyon degeneracies from Mathieu moonshine
• Second Quantized Mathieu Moonshine
• Mathieu Moonshine and Symmetry Surfing
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• On the elliptic genera of manifolds of Spin(7) holonomy
• Not Doomed to Fail
• Conway Subgroup Symmetric Compactifications Redux
• Mathieu Moonshine and Siegel Modular Forms
• Some comments on symmetric orbifolds of K3
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results