Duality defects in E ₈

We classify all non-invertible Kramers-Wannier duality defects in the E₈ lattice Vertex Operator Algebra (i.e. the chiral (E₈)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.