期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 4, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP04(2022)138
关键词
Anyons; Topological States of Matter; Gauge Symmetry
资金
- Sun Yat-sen University Talent Plan
- Guangdong Basic and Applied Basic Research Foundation [2020B1515120100]
- National Natural Science Foundation of China (NSFC) [11847608, 12074438]
The paper presents a topological quantum field theoretical study on topological orders in five-dimensional spacetime, introducing higher-form gauge fields and constructing exotic TQFT actions. The characterization and classification of 5D topological orders encode information of 4D gravitational anomaly, and further research on putting TQFTs on 5D manifolds with boundaries is suggested.
Topological orders are a prominent paradigm for describing quantum manybody systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime (5D) in which topological excitations include not only point-like particles, but also two types of spatially extended objects: closed string-like loops and two-dimensional closed membranes. Especially, membranes have been rarely explored in the literature of topological orders. By introducing higher-form gauge fields, we construct exotic TQFT actions that include mixture of two distinct types of BF topological terms and many twisted topological terms. The gauge transformations are properly defined and utilized to compute level quantization and classification of TQFTs. Among all TQFTs, some are not in Dijkgraaf-Witten cohomological classification. To characterize topological orders, we concretely construct all braiding processes among topological excitations, which leads to very exotic links formed by closed spacetime trajectories of particles, loops, and membranes. For each braiding process, we construct gauge-invariant Wilson operators and calculate the associated braiding statistical phases. As a result, we obtain expressions of link invariants all of which have manifest geometric interpretation. Following Wen's definition, the boundary theory of a topological order exhibits gravitational anomaly. We expect that the characterization and classification of 5D topological orders in this paper encode information of 4D gravitational anomaly. Further consideration, e.g., putting TQFTs on 5D manifolds with boundaries, is left to future work.
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