We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.
In this short note, we comment on the existence of two more fermionic unitary minimal models not included in recent work by Hsieh, Nakayama, and Tachikawa. These theories are obtained by fermionizing the ℤ2 symmetry of the m = 11 and m = 12 exceptional unitary minimal models. Furthermore, we explain why these are the only missing cases.
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 ℤm 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.
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