Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
Invariants of Piecewise-Linear 3-Manifolds
9 Pith papers cite this work, alongside 325 external citations. Polarity classification is still indexing.
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abstract
In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple involutory Hopf algebra. The invariant is defined by a state sum model on a triangulation. In some cases, the invariant is the partition function of a topological quantum field theory.
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Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
A sparse cyclotomic-exponent representation of q-hypergeometric series defers evaluation and performs cancellations exactly, improving memory and precision for quantum 6j-symbol computations.
citing papers explorer
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Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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ASEP/DSSYK duality and strange correlator
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
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Deferred Cyclotomic Representation for Stable and Exact Evaluation of q-Hypergeometric Series
A sparse cyclotomic-exponent representation of q-hypergeometric series defers evaluation and performs cancellations exactly, improving memory and precision for quantum 6j-symbol computations.