New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
Braided tensor categories and extensions of vertex operator algebras
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abstract
Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions of extension (i.e., enlargement) of $V$ and of commutative associative algebra, with uniqueness of unit and with trivial twist, in the braided tensor category of $V$-modules are equivalent.
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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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Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
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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.