Duality defects in E8

doi:10.1007/JHEP10(2022)187

Duality defects in E8

2022-10-28

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DOI：10.1007/JHEP10(2022)187

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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 DOUBLE-STRUCK CAPITAL Z(m) symmetries. We illustrate how these defects are systematically obtainable as DOUBLE-STRUCK CAPITAL Z(2) 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

Duality defects in E8

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