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 …
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 …
(3+1)D topological orders with only a -charged particle
T Johnson-Freyd - arXiv preprint arXiv:2011.11165, 2020 - arxiv.org
There is exactly one bosonic (3+ 1)-dimensional topological order whose only nontrivial
particle is an emergent boson: pure $\mathbb {Z} _2 $ gauge theory. There are exactly two …
particle is an emergent boson: pure $\mathbb {Z} _2 $ gauge theory. There are exactly two …
On dualizability of braided tensor categories
We study the question of dualizability in higher Morita categories of locally presentable
tensor categories and braided tensor categories. Our main results are that the 3-category of …
tensor categories and braided tensor categories. Our main results are that the 3-category of …
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 …
A classification of modular functors via factorization homology
A Brochier, L Woike - arXiv preprint arXiv:2212.11259, 2022 - arxiv.org
Modular functors are traditionally defined as systems of projective representations of
mapping class groups of surfaces that are compatible with gluing. They can formally be …
mapping class groups of surfaces that are compatible with gluing. They can formally be …
Bosonization and Anomaly Indicators of (2+ 1)-D Fermionic Topological Orders
We provide a mathematical proposal for the anomaly indicators of symmetries of (2+ 1)-d
fermionic topological orders, and work out the consequences of our proposal in several …
fermionic topological orders, and work out the consequences of our proposal in several …
Compact semisimple 2-categories
T Décoppet - Transactions of the American Mathematical Society, 2023 - ams.org
Working over an arbitrary field, we define compact semisimple 2-categories, and show that
every compact semisimple 2-category is equivalent to the 2-category of separable module 1 …
every compact semisimple 2-category is equivalent to the 2-category of separable module 1 …
Cyclic framed little disks algebras, Grothendieck–Verdier duality and handlebody group representations
We characterize cyclic algebras over the associative and the framed little 2-disks operad in
any symmetric monoidal bicategory. The cyclicity is appropriately treated in a coherent way …
any symmetric monoidal bicategory. The cyclicity is appropriately treated in a coherent way …