Duality defects in E 8

Abstract

Abstract We classify all non-invertible Kramers-Wannier duality defects in the E 8 lattice Vertex Operator Algebra (i.e. the chiral (E 8)1 WZW model) coming from ℤ m symmetries. We illustrate how these defects are systematically obtainable as ℤ2 twists of invariant sub-VOAs, compute defect partition functions for small m, and verify our results against other techniques. Throughout, we focus on taking a physical perspective and highlight the important moving pieces involved in the calculations. Kac’s theorem for finite automorphisms of Lie algebras and contemporary results on holomorphic VOAs play a role. We also provide a perspective from the point of view of (2+1)d Topological Field Theory and provide a rigorous proof that all corresponding Tambara-Yamagami actions on holomorphic VOAs can be obtained in this manner. We include a list of directions for future studies.

Keywords

• Discrete Symmetries
• Global Symmetries
• Anomalies in Field and String Theories