期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 3, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP03(2018)189
关键词
Anyons; Discrete Symmetries; Global Symmetries; Topological Field Theories
资金
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through Ministry of Economic Development and Innovation
- JSPS KAKENHI [17H04837, 16H06335]
- WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo
It is well-known that if we gauge a Z(n) symmetry in two dimensions, a dual Z(n) symmetry appears, such that re-gauging this dual Z(n) symmetry leads back to the original theory. We describe how this can be generalized to non-Abelian groups, by enlarging the concept of symmetries from those defined by groups to those defined by unitary fusion categories. We will see that this generalization is also useful when studying what happens when a non-anomalous subgroup of an anomalous finite group is gauged: for example, the gauged theory can have non-Abelian group symmetry even when the original symmetry is an Abelian group. We then discuss the axiomatization of two-dimensional topological quantum field theories whose symmetry is given by a category. We see explicitly that the gauged version is a topological quantum field theory with a new symmetry given by a dual category.
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