Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
Volpato, Vertex algebras, topological defects, and Moonshine , http://arxiv.org/abs/2412.21141 arXiv:2412.21141 [hep-th]
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Assuming a conjectural decomposition of the Monster character, the Monster CFT has Rep(so(3)_p) symmetry for every odd prime p, and the associated defect McKay-Thompson series have invariance subgroup Γ1(p+2).
Hodge loci in Calabi-Yau sigma models are identified with non-trivial categories of topological defects preserving N=(2,2) SCA and invertible on spectral-flow generators, with CM structure at special points.
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Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left-right symmetries and boundary conditions in 2D CFTs.
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Parafermionizing the Monster
Assuming a conjectural decomposition of the Monster character, the Monster CFT has Rep(so(3)_p) symmetry for every odd prime p, and the associated defect McKay-Thompson series have invariance subgroup Γ1(p+2).
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Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Hodge loci in Calabi-Yau sigma models are identified with non-trivial categories of topological defects preserving N=(2,2) SCA and invertible on spectral-flow generators, with CM structure at special points.