Homotopy theory of algebraic quantum field theories
M Benini, A Schenkel, L Woike - Letters in Mathematical Physics, 2019 - Springer
Motivated by gauge theory, we develop a general framework for chain complex-valued
algebraic quantum field theories. Building upon our recent operadic approach to this …
algebraic quantum field theories. Building upon our recent operadic approach to this …
Higher Structures in Algebraic Quantum Field Theory: LMS/EPSRC Durham Symposium on Higher Structures in M‐Theory
M Benini, A Schenkel - Fortschritte der Physik, 2019 - Wiley Online Library
Higher Structures in Algebraic Quantum Field Theory - Benini - 2019 - Fortschritte der Physik -
Wiley Online Library Skip to Article Content Skip to Article Information Wiley Online Library …
Wiley Online Library Skip to Article Content Skip to Article Information Wiley Online Library …
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 …
Orbifolds of Reshetikhin-Turaev TQFTs
N Carqueville, I Runkel, G Schaumann - arXiv preprint arXiv:1809.01483, 2018 - arxiv.org
We construct three classes of generalised orbifolds of Reshetikhin-Turaev theory for a
modular tensor category $\mathcal {C} $, using the language of defect TQFT from [arXiv …
modular tensor category $\mathcal {C} $, using the language of defect TQFT from [arXiv …
Homotopy coherent mapping class group actions and excision for Hochschild complexes of modular categories
C Schweigert, L Woike - Advances in Mathematics, 2021 - Elsevier
Given any modular category C over an algebraically closed field k, we extract a sequence
(M g) g≥ 0 of C-bimodules and show that the Hochschild chain complex CH (C; M g) of C …
(M g) g≥ 0 of C-bimodules and show that the Hochschild chain complex CH (C; M g) of C …
Semisimple field theories detect stable diffeomorphism
D Reutter, C Schommer-Pries - arXiv preprint arXiv:2206.10031, 2022 - arxiv.org
Extending the work of the first author, we introduce a notion of semisimple topological field
theory in arbitrary even dimension and show that such field theories necessarily lead to …
theory in arbitrary even dimension and show that such field theories necessarily lead to …
Orbifold graph TQFTs
N Carqueville, V Mulevicius, I Runkel… - arXiv preprint arXiv …, 2021 - arxiv.org
A generalised orbifold of a defect TQFT $\mathcal {Z} $ is another TQFT $\mathcal {Z} _
{\mathcal {A}} $ obtained by performing a state sum construction internal to $\mathcal {Z} …
{\mathcal {A}} $ obtained by performing a state sum construction internal to $\mathcal {Z} …
The Hochschild complex of a finite tensor category
C Schweigert, L Woike - Algebraic & Geometric Topology, 2021 - msp.org
Modular functors, ie consistent systems of projective representations of mapping class
groups of surfaces, were constructed for nonsemisimple modular categories decades ago …
groups of surfaces, were constructed for nonsemisimple modular categories decades ago …
Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf–Witten theory
MB Young - Communications in Mathematical Physics, 2020 - Springer
Given a finite Z _2 Z 2-graded group ̂ GG^ with ungraded subgroup GG and a twisted
cocycle ̂ λ ∈ Z^ n (B ̂ G; U (1) _ π) λ^∈ Z n (BG^; U (1) π) which restricts to λ ∈ Z^ n (BG; …
cocycle ̂ λ ∈ Z^ n (B ̂ G; U (1) _ π) λ^∈ Z n (BG^; U (1) π) which restricts to λ ∈ Z^ n (BG; …
On 3-dimensional homotopy quantum field theory III: comparison of two approaches
V Turaev, A Virelizier - International Journal of Mathematics, 2020 - World Scientific
On 3-dimensional homotopy quantum field theory III: Comparison of two approaches Page 1
International Journal of Mathematics Vol. 31, No. 10 (2020) 2050076 (57 pages) c World …
International Journal of Mathematics Vol. 31, No. 10 (2020) 2050076 (57 pages) c World …