On reconstructing finite gauge group from fusion rules
Abstract Gauging a finite group 0-form symmetry G of a quantum field theory (QFT) results in a QFT with a Rep(G) symmetry implemented by Wilson lines. The group G determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine G. In this paper, we study...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-02-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2024)043 |
| _version_ | 1827214431577178112 |
|---|---|
| author | Rajath Radhakrishnan |
| author_facet | Rajath Radhakrishnan |
| author_sort | Rajath Radhakrishnan |
| collection | DOAJ |
| description | Abstract Gauging a finite group 0-form symmetry G of a quantum field theory (QFT) results in a QFT with a Rep(G) symmetry implemented by Wilson lines. The group G determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine G. In this paper, we study the properties of G 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. |
| first_indexed | 2024-03-07T15:23:40Z |
| format | Article |
| id | doaj.art-39295b2a75a64448aefb19ab112eb2a6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T14:31:13Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-39295b2a75a64448aefb19ab112eb2a62024-06-23T11:07:25ZengSpringerOpenJournal of High Energy Physics1029-84792024-02-012024213910.1007/JHEP02(2024)043On reconstructing finite gauge group from fusion rulesRajath Radhakrishnan0Abdus Salam International Centre for Theoretical PhysicsAbstract Gauging a finite group 0-form symmetry G of a quantum field theory (QFT) results in a QFT with a Rep(G) symmetry implemented by Wilson lines. The group G determines the fusion of Wilson lines. However, in general, the fusion rules of Wilson lines do not determine G. In this paper, we study the properties of G 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.https://doi.org/10.1007/JHEP02(2024)043Discrete SymmetriesGauge SymmetryGlobal SymmetriesField Theories in Lower Dimensions |
| spellingShingle | Rajath Radhakrishnan On reconstructing finite gauge group from fusion rules Journal of High Energy Physics Discrete Symmetries Gauge Symmetry Global Symmetries Field Theories in Lower Dimensions |
| title | On reconstructing finite gauge group from fusion rules |
| title_full | On reconstructing finite gauge group from fusion rules |
| title_fullStr | On reconstructing finite gauge group from fusion rules |
| title_full_unstemmed | On reconstructing finite gauge group from fusion rules |
| title_short | On reconstructing finite gauge group from fusion rules |
| title_sort | on reconstructing finite gauge group from fusion rules |
| topic | Discrete Symmetries Gauge Symmetry Global Symmetries Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP02(2024)043 |
| work_keys_str_mv | AT rajathradhakrishnan onreconstructingfinitegaugegroupfromfusionrules |