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Orbifolds of n-dimensional defect TQFTs. (arXiv:1705.06085v1 [math.QA])
来源于:arXiv
We introduce the notion of $n$-dimensional topological quantum field theory
(TQFT) with defects as a symmetric monoidal functor on decorated stratified
bordisms of dimension $n$. The familiar closed or open-closed TQFTs are special
cases of defect TQFTs, and for $n=2$ and $n=3$ our general definition recovers
what had previously been studied in the literature.
Our main construction is that of "generalised orbifolds" for any
$n$-dimensional defect TQFT: Given a defect TQFT $\mathcal{Z}$, one obtains a
new TQFT $\mathcal{Z}_{\mathcal{A}}$ by decorating the Poincar\'e duals of
triangulated bordisms with certain algebraic data $\mathcal{A}$ and then
evaluating with $\mathcal{Z}$. The orbifold datum $\mathcal{A}$ is constrained
by demanding invariance under $n$-dimensional Pachner moves. This procedure
generalises both state sum models and gauging of finite symmetry groups, for
any $n$. After developing the general theory, we focus on the case $n=3$. 查看全文>>