Topological orders and factorization homology
Topological orders and factorization homology
复制标题
拓扑序和因式分解同源性
DOI：
10.4310/atmp.2017.v21.n8.a1
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发表时间：
2016-07
影响因子：
1.5
通讯作者：
Hao Zheng
中科院分区：
文献类型：
--
作者：
Yinhua Ai;Liang Kong;Hao Zheng
In the study of 2d (the space dimension) topological orders, it is well-known that bulk excitations are classified by unitary modular tensor categories. But these categories only describe the local observables on an open 2-disk in the long wave length limit. For example, the notion of braiding only makes sense locally. It is natural to ask how to obtain global observables on a closed surface. The answer is provided by the theory of factorization homology. We compute the factorization homology of a closed surface $\Sigma$ with the coefficient given by a unitary modular tensor category, and show that the result is given by a pair $(\mathbf{H}, u_\Sigma)$, where $\mathbf{H}$ is the category of finite-dimensional Hilbert spaces and $u_\Sigma\in \mathbf{H}$ is a distinguished object that coincides precisely with the Hilbert space assigned to the surface $\Sigma$ in Reshetikhin-Turaev TQFT. We also generalize this result to a closed stratified surface decorated by anomaly-free topological defects of codimension 0,1,2. This amounts to compute the factorization homology of a stratified surface with a coefficient system satisfying an anomaly-free condition.
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DOI：
--
发表时间：
2014-05
期刊：
arXiv: Strongly Correlated Electrons
影响因子：
--
作者：
Liang Kong;X. Wen
通讯作者：
Liang Kong;X. Wen
DOI：
10.4153/cmb-2013-017-5
发表时间：
2012-09
期刊：
Canadian Mathematical Bulletin
影响因子：
--
作者：
César Galindo
通讯作者：
César Galindo
影响因子：
2
作者：
Christopher J. Schommer-Pries
通讯作者：
Christopher J. Schommer-Pries
影响因子：
3.7
作者：
Yuting Hu;S. D. Stirling;Yong-Shi Wu
通讯作者：
Yuting Hu;S. D. Stirling;Yong-Shi Wu
影响因子：
1.1
作者：
David Ayala;J. Francis
通讯作者：
David Ayala;J. Francis