On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds
Abstract We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in SU(n) or U(n) gauge theories compactified on the orbifolds T 2 /ℤ N (N = 2, 3, 4, 6). We suppose that the theory has a global G′ = U(n) symmetry. Using constrain...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2023)113 |
| _version_ | 1797769713953013760 |
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| author | Yoshiharu Kawamura Eiji Kodaira Kentaro Kojima Toshifumi Yamashita |
| author_facet | Yoshiharu Kawamura Eiji Kodaira Kentaro Kojima Toshifumi Yamashita |
| author_sort | Yoshiharu Kawamura |
| collection | DOAJ |
| description | Abstract We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in SU(n) or U(n) gauge theories compactified on the orbifolds T 2 /ℤ N (N = 2, 3, 4, 6). We suppose that the theory has a global G′ = U(n) symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on T 2 /ℤ2 and T 2 /ℤ3, but the representation matrices on T 2 /ℤ4 and T 2 /ℤ6 can contain not only diagonal matrices but also non-diagonal 2 × 2 ones and non-diagonal 3 × 3 and 2 × 2 ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases. |
| first_indexed | 2024-03-12T21:11:58Z |
| format | Article |
| id | doaj.art-70421168680f4835837cd4539c5d5b21 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T21:11:58Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-70421168680f4835837cd4539c5d5b212023-07-30T11:04:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-04-012023415710.1007/JHEP04(2023)113On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifoldsYoshiharu Kawamura0Eiji Kodaira1Kentaro Kojima2Toshifumi Yamashita3Department of Physics, Shinshu UniversityDepartment of Physics, Shinshu UniversityFaculty of Arts and Science, Kyushu UniversityDepartment of Physics, Aichi Medical UniversityAbstract We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in SU(n) or U(n) gauge theories compactified on the orbifolds T 2 /ℤ N (N = 2, 3, 4, 6). We suppose that the theory has a global G′ = U(n) symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on T 2 /ℤ2 and T 2 /ℤ3, but the representation matrices on T 2 /ℤ4 and T 2 /ℤ6 can contain not only diagonal matrices but also non-diagonal 2 × 2 ones and non-diagonal 3 × 3 and 2 × 2 ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases.https://doi.org/10.1007/JHEP04(2023)113Extra DimensionsField Theories in Higher DimensionsGrand Unification |
| spellingShingle | Yoshiharu Kawamura Eiji Kodaira Kentaro Kojima Toshifumi Yamashita On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds Journal of High Energy Physics Extra Dimensions Field Theories in Higher Dimensions Grand Unification |
| title | On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds |
| title_full | On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds |
| title_fullStr | On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds |
| title_full_unstemmed | On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds |
| title_short | On representation matrices of boundary conditions in SU(n) gauge theories compactified on two-dimensional orbifolds |
| title_sort | on representation matrices of boundary conditions in su n gauge theories compactified on two dimensional orbifolds |
| topic | Extra Dimensions Field Theories in Higher Dimensions Grand Unification |
| url | https://doi.org/10.1007/JHEP04(2023)113 |
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