Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications
We give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an exa...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics Proceedings |
| Online Access: | https://scipost.org/SciPostPhysProc.14.016 |
| _version_ | 1827660233983393792 |
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| author | Naruhiko Aizawa |
| author_facet | Naruhiko Aizawa |
| author_sort | Naruhiko Aizawa |
| collection | DOAJ |
| description | We give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$-graded SUSY classical actions are constructed. |
| first_indexed | 2024-03-09T23:40:08Z |
| format | Article |
| id | doaj.art-a4f1eeaff9fd4210bd8526167d70c61c |
| institution | Directory Open Access Journal |
| issn | 2666-4003 |
| language | English |
| last_indexed | 2024-03-09T23:40:08Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Proceedings |
| spelling | doaj.art-a4f1eeaff9fd4210bd8526167d70c61c2023-11-23T16:53:34ZengSciPostSciPost Physics Proceedings2666-40032023-11-011401610.21468/SciPostPhysProc.14.016Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applicationsNaruhiko AizawaWe give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$-graded SUSY classical actions are constructed.https://scipost.org/SciPostPhysProc.14.016 |
| spellingShingle | Naruhiko Aizawa Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications SciPost Physics Proceedings |
| title | Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications |
| title_full | Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications |
| title_fullStr | Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications |
| title_full_unstemmed | Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications |
| title_short | Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications |
| title_sort | irreducible representations of mathbb z 2 2 graded supersymmetry algebra and their applications |
| url | https://scipost.org/SciPostPhysProc.14.016 |
| work_keys_str_mv | AT naruhikoaizawa irreduciblerepresentationsofmathbbz22gradedsupersymmetryalgebraandtheirapplications |