Topological symmetry in quantum field theory
DS Freed, GW Moore, C Teleman - arXiv preprint arXiv:2209.07471, 2022 - arxiv.org
We introduce a framework for internal topological symmetries in quantum field theory,
including" noninvertible symmetries" and" categorical symmetries". This leads to a calculus …
including" noninvertible symmetries" and" categorical symmetries". This leads to a calculus …
Fusion 2-categories and a state-sum invariant for 4-manifolds
CL Douglas, DJ Reutter - arXiv preprint arXiv:1812.11933, 2018 - arxiv.org
arXiv:1812.11933v1 [math.QA] 31 Dec 2018 Page 1 FUSION 2-CATEGORIES AND A
STATE-SUM INVARIANT FOR 4-MANIFOLDS CHRISTOPHER L. DOUGLAS AND DAVID J …
STATE-SUM INVARIANT FOR 4-MANIFOLDS CHRISTOPHER L. DOUGLAS AND DAVID J …
Minimal nondegenerate extensions
T Johnson-Freyd, D Reutter - Journal of the American Mathematical Society, 2024 - ams.org
We prove that every slightly degenerate braided fusion category admits a minimal
nondegenerate extension, and hence that every pseudo-unitary super modular tensor …
nondegenerate extension, and hence that every pseudo-unitary super modular tensor …
An invitation to topological orders and category theory
L Kong, ZH Zhang - arXiv preprint arXiv:2205.05565, 2022 - arxiv.org
Although it has been a well-known fact, for more than two decades, that category theory is
needed for the study of topological orders, it is still a non-trivial challenge for students and …
needed for the study of topological orders, it is still a non-trivial challenge for students and …
[HTML][HTML] The finiteness conjecture for skein modules
The finiteness conjecture for skein modules | Inventiones mathematicae Skip to main content
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
SpringerLink Account Menu Find a journal Publish with us Track your research Search Cart …
Integrating quantum groups over surfaces
We apply the mechanism of factorization homology to construct and compute category‐
valued two‐dimensional topological field theories associated to braided tensor categories …
valued two‐dimensional topological field theories associated to braided tensor categories …
Gapped boundary theories in three dimensions
DS Freed, C Teleman - Communications in Mathematical Physics, 2021 - Springer
We prove a theorem in 3-dimensional topological field theory: a Reshetikhin–Turaev theory
admits a nonzero boundary theory iff it is a Turaev–Viro theory. The proof immediately …
admits a nonzero boundary theory iff it is a Turaev–Viro theory. The proof immediately …
[HTML][HTML] Rigid and separable algebras in fusion 2-categories
TD Décoppet - Advances in Mathematics, 2023 - Elsevier
Rigid monoidal 1-categories are ubiquitous throughout quantum algebra and low-
dimensional topology. We study a generalization of this notion, namely rigid algebras in an …
dimensional topology. We study a generalization of this notion, namely rigid algebras in an …
Orbifold completion of 3-categories
N Carqueville, L Müller - arXiv preprint arXiv:2307.06485, 2023 - arxiv.org
We develop a general theory of 3-dimensional``orbifold completion'', to describe
(generalised) orbifolds of topological quantum field theories as well as all their defects …
(generalised) orbifolds of topological quantum field theories as well as all their defects …
Composing topological domain walls and anyon mobility
Topological domain walls separating 2+ 1 dimensional topologically ordered phases can be
understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk …
understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk …