On Reconstructing Finite Gauge Group from Fusion Rules
Feb 16, 2023Citations per year
Abstract: (arXiv)
Gauging a finite group 0-form symmetry of a quantum field theory (QFT) results in a QFT with a Rep symmetry implemented by Wilson lines. The group determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine . In this paper, we study the properties of that can be determined from the fusion rules of Wilson lines and surface operators obtained from higher-gauging Wilson lines. This is in the spirit of Richard Brauer who asked what information in addition to the character table of a finite group needs to be known to determine the group. We show that fusion rules of surface operators obtained from higher-gauging Wilson lines can be used to distinguish infinite pairs of groups which cannot be distinguished using the fusion of Wilson lines. We derive necessary conditions for two non-isomorphic groups to have the same surface operator fusion and find a pair of such groups.Note:
- 45 pages, 7 figures
- operator: surface
- group: finite
- fusion
- Wilson loop
References(53)
Figures(0)
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- [1]
- [2]
- [2]
- [3]
- [4]
- [4]
- [4]
- [4]
- [5]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [15]
- [16]
- [17]
- [18]