Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness, and rigidity assumptions.
Generalized Tube Algebras, Symmetry-Resolved Partition Functions, and Twisted Boundary States,
7 Pith papers cite this work. Polarity classification is still indexing.
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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.
Constructs a family of non-invertible topological defects in n Weyl fermion theories via unfolding of G-symmetric boundary conditions for Dirac fermions, with explicit descriptions for U(1)^n and applications to fermion-boundary scattering.
Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.