On Reconstructing Finite Gauge Group from Fusion Rules

Feb 16, 2023
45 pages
Published in:
  • JHEP 2024 (2024) 02, 043
e-Print:

Citations per year

202220232024052
Abstract: (arXiv)
Gauging a finite group 0-form symmetry GG of a quantum field theory (QFT) results in a QFT with a Rep(G)(G) symmetry implemented by Wilson lines. The group GG determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine GG. In this paper, we study the properties of GG 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