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.
Regularity of fixed-point vertex operator subalgebras
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show that if $T$ is a simple non-negatively graded regular vertex operator algebra with a nonsingular invariant bilinear form and $\sigma$ is a finite order automorphism of $T$, then the fixed-point vertex operator subalgebra $T^\sigma$ is also regular. This yields regularity for fixed point vertex operator subalgebras under the action of any finite solvable group. As an application, we obtain an $SL_2(\mathbb{Z})$-compatibility between twisted twining characters for commuting finite order automorphisms of holomorphic vertex operator algebras. This resolves one of the principal claims in the Generalized Moonshine conjecture.
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Proves holonomicity of conformal blocks sheaves and that flat sections are spanned by trace functions for quasi-lisse vertex algebras satisfying finiteness and semisimplicity, generalizing Zhu's theorem with a dimension coincidence for admissible affine cases.
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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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Modular invariance of characters of quasi-lisse vertex algebras
Proves holonomicity of conformal blocks sheaves and that flat sections are spanned by trace functions for quasi-lisse vertex algebras satisfying finiteness and semisimplicity, generalizing Zhu's theorem with a dimension coincidence for admissible affine cases.