3-dimensional defect TQFTs and their tricategories
Quantum Algebra
2021-01-20 v2 High Energy Physics - Theory
Mathematical Physics
Category Theory
math.MP
Abstract
We initiate a systematic study of 3-dimensional `defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is the natural categorification of a pivotal bicategory. This captures the algebraic essence of defect TQFTs, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations. As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can be extended to defect TQFTs.
Cite
@article{arxiv.1603.01171,
title = {3-dimensional defect TQFTs and their tricategories},
author = {Nils Carqueville and Catherine Meusburger and Gregor Schaumann},
journal= {arXiv preprint arXiv:1603.01171},
year = {2021}
}
Comments
60 pages; v2: improved exposition