Commutative exact algebras and modular tensor categories
K Shimizu, H Yadav - arXiv preprint arXiv:2408.06314, 2024 - arxiv.org
Inspired by the study of vertex operator algebra extensions, we answer the question of when
the category of local modules over a commutative exact algebra in a braided finite tensor …
the category of local modules over a commutative exact algebra in a braided finite tensor …
CFT correlators and mapping class group averages
I Romaidis, I Runkel - Communications in Mathematical Physics, 2024 - Springer
Mapping class group averages appear in the study of 3D gravity partition functions. In this
paper, we work with 3D topological field theories to establish a bulk-boundary …
paper, we work with 3D topological field theories to establish a bulk-boundary …
Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
T Creutzig, R McRae, K Shimizu, H Yadav - arXiv preprint arXiv …, 2024 - arxiv.org
Let $ A $ be a commutative algebra in a braided monoidal category $\mathcal {C} $; eg, $ A
$ could be an extension of a vertex operator algebra (VOA) $ V $ in a category $\mathcal {C} …
$ could be an extension of a vertex operator algebra (VOA) $ V $ in a category $\mathcal {C} …
Invertible braided tensor categories
We prove that a finite braided tensor category 𝒜 is invertible in the Morita 4–category BrTens
of braided tensor categories if and only if it is nondegenerate. This includes the case of …
of braided tensor categories if and only if it is nondegenerate. This includes the case of …
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 …
Homological construction of quantum representations of mapping class groups
M De Renzi, J Martel - arXiv preprint arXiv:2212.10940, 2022 - arxiv.org
We provide a homological model for a family of quantum representations of mapping class
groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our …
groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our …
tilting modules in the mixed case
Using the non-semisimple Temperley–Lieb calculus, we study the additive and monoidal
structure of the category of tilting modules for SL 2 in the mixed case. This simultaneously …
structure of the category of tilting modules for SL 2 in the mixed case. This simultaneously …
Mapping class group representations from non-semisimple TQFTs
In [M. De Renzi, A. Gainutdinov, N. Geer, B. Patureau-Mirand and I. Runkel, 3-dimensional
TQFTs from non-semisimple modular categories, preprint (2019), arXiv: 1912.02063 [math …
TQFTs from non-semisimple modular categories, preprint (2019), arXiv: 1912.02063 [math …
Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories
Hecke operators relate characters of rational conformal field theories (RCFTs) with different
central charges, and extend the previously studied Galois symmetry of modular …
central charges, and extend the previously studied Galois symmetry of modular …
Reshetikhin–Turaev TQFTs close under generalised orbifolds
N Carqueville, V Mulevičius, I Runkel… - … in Mathematical Physics, 2024 - Springer
We specialise the construction of orbifold graph TQFTs introduced in Carqueville et
al.(Orbifold graph TQFTs) to Reshetikhin–Turaev defect TQFTs. We explain that the modular …
al.(Orbifold graph TQFTs) to Reshetikhin–Turaev defect TQFTs. We explain that the modular …