Duality defects in E 8

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...

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Bibliographic Details
Published in:The journal of high energy physics 2022-10, Vol.2022 (10), p.1-64
Main Authors: Ivan M. Burbano, Justin Kulp, Jonas Neuser
Format: Article
Language:English
Subjects:
Anomalies in Field and String Theories
Discrete Symmetries
Global Symmetries
Online Access:Get full text
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Summary: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.
ISSN:1029-8479
DOI:10.1007/JHEP10(2022)187