报告题目: |
A categorical theory of topological orders of all dimensions (d > -1) |
报告人: |
Liang Kong |
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IAS at Tsinghua University and University of New Hampshire
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报告时间: |
2015-05-29 10:00 |
报告地点: |
Conference Hall 322, Science Building, Tsinghua University |
主办单位: |
高等研究院 |
简介: |
I will start with the motivation to study the category of topological orders. It is important to distinguish a topological order defined on an open disk, called a local topological order, and that on a closed manifold. By focusing on only local topological order, we naturally obtain the notion of an (unitary) n-category, in which 1-morphisms are defects of codimension 1, 2-morphisms are defects of codimension 2, so on and so forth. I will discuss some low dimensional cases. For n>2, it becomes difficult to discuss explicit examples. It seems that it is very difficult to go further with these abstract nonsense. However, I will argue that if a local topological order allows a gapped boundary, then it is uniquely determined by the boundary. This uniqueness of the bulk has deep consequences. For example, it implies that the unique bulk of a given boundary is given by the mathematical center of the boundary. Moreover, it also leads us to a condensation theory as a theory of ``linear algebras" over higher categories. It is a join work with Xiao-Gang Wen and Hao Zheng. |
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