On finite symmetries and their gauging in two dimensions
Abstract 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 de...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-03-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2018)189 |
| _version_ | 1831724528320905216 |
|---|---|
| author | Lakshya Bhardwaj Yuji Tachikawa |
| author_facet | Lakshya Bhardwaj Yuji Tachikawa |
| author_sort | Lakshya Bhardwaj |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-21T04:23:12Z |
| format | Article |
| id | doaj.art-9e7d54ce19cc4423b362e3a45e15107b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T04:23:12Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9e7d54ce19cc4423b362e3a45e15107b2022-12-21T19:16:07ZengSpringerOpenJournal of High Energy Physics1029-84792018-03-012018316810.1007/JHEP03(2018)189On finite symmetries and their gauging in two dimensionsLakshya Bhardwaj0Yuji Tachikawa1Perimeter Institute for Theoretical PhysicsKavli Institute for the Physics and Mathematics of the Universe, University of TokyoAbstract 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.http://link.springer.com/article/10.1007/JHEP03(2018)189AnyonsDiscrete SymmetriesGlobal SymmetriesTopological Field Theories |
| spellingShingle | Lakshya Bhardwaj Yuji Tachikawa On finite symmetries and their gauging in two dimensions Journal of High Energy Physics Anyons Discrete Symmetries Global Symmetries Topological Field Theories |
| title | On finite symmetries and their gauging in two dimensions |
| title_full | On finite symmetries and their gauging in two dimensions |
| title_fullStr | On finite symmetries and their gauging in two dimensions |
| title_full_unstemmed | On finite symmetries and their gauging in two dimensions |
| title_short | On finite symmetries and their gauging in two dimensions |
| title_sort | on finite symmetries and their gauging in two dimensions |
| topic | Anyons Discrete Symmetries Global Symmetries Topological Field Theories |
| url | http://link.springer.com/article/10.1007/JHEP03(2018)189 |
| work_keys_str_mv | AT lakshyabhardwaj onfinitesymmetriesandtheirgaugingintwodimensions AT yujitachikawa onfinitesymmetriesandtheirgaugingintwodimensions |