On symmetries of N=(4,4) sigma models on T^4

Abstract

Motivated by an analogous result for K3 models, we classify all groups of symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4) superconformal algebra. The resulting symmetry groups are isomorphic to certain subgroups of the Weyl group of E8, that plays a role similar to the Conway group for the case of K3 models. Our analysis heavily relies on the triality automorphism of the T-duality group SO(4,4,Z). As a byproduct of our results, we discover new explicit descriptions of K3 models as asymmetric orbifolds of torus CFTs.

arXiv comment42 pages; minor changes, references added; version accepted for publication

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• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• K3 String Theory, Lattices and Moonshine
• Finite groups of symplectic automorphisms of hyperkähler manifolds of type $K{3}^{[2]}$
• Mathieu Moonshine and Symmetry Surfing
• Symmetries of the refined D1/D5 BPS spectrum
• Not Doomed to Fail
• Conway Subgroup Symmetric Compactifications Redux
• Vertex operator superalgebra/sigma model correspondences: The four-torus case
• Some comments on symmetric orbifolds of K3
• A plethora of K3 metrics
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups