Modern Tensor-Spinor Symbolic Algebra Algorithms and Computing Non-Closure Geometry & Holoraumy in 11D, N = 1 Supergravity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913412298047488 |
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| author | Gates Jr., S. James Hilsenrath, Isaiah B. Hilsenrath, Saul |
| author_facet | Gates Jr., S. James Hilsenrath, Isaiah B. Hilsenrath, Saul |
| contents | The Supersymmetry Genomics project aims to classify supermultiplets by properties like adinkras and holoraumy. The project's protocol is: 1) set up the SUSY transformation rules (and action) with unknown numerical coefficients, 2) solve those coefficients, and 3) compute desired properties, e.g., non-closure geometry (the non-closure functions in the anticommutator of supercovariant derivatives) and holoraumy (the commutator of supercovariant derivatives). This paper provides the first broadly applicable computer algorithms for completing these computations, comprising a new Cadabra module we call ``SusyPy.'' We provide a significant extension of the available tensor-arithmetic/canonicalization to include spinor-indexed expressions and NW-SE convention, and we provide a new Fierz expansion algorithm for spinor-indexed expressions. On top of this new tensor-spinor symbolic algebra, we have built algorithms for solving for the coefficients of a multiplet and its action, and for computing holoraumy, for both off-shell and on-shell N = 1 multiplets of any dimension. We apply our tools to assimilate linearized 11D, N = 1 supergravity into the Genomics project. We demonstrate solving the 11D, N = 1 multiplet, as in Cremmer, Julia, and Scherk, in a few lines of code, and we provide a comprehensive picture of the multiplet's non-closure geometry. Further, we provide the first-ever computation of the holoraumy of 11D, N = 1 supergravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00614 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Modern Tensor-Spinor Symbolic Algebra Algorithms and Computing Non-Closure Geometry & Holoraumy in 11D, N = 1 Supergravity Gates Jr., S. James Hilsenrath, Isaiah B. Hilsenrath, Saul High Energy Physics - Theory The Supersymmetry Genomics project aims to classify supermultiplets by properties like adinkras and holoraumy. The project's protocol is: 1) set up the SUSY transformation rules (and action) with unknown numerical coefficients, 2) solve those coefficients, and 3) compute desired properties, e.g., non-closure geometry (the non-closure functions in the anticommutator of supercovariant derivatives) and holoraumy (the commutator of supercovariant derivatives). This paper provides the first broadly applicable computer algorithms for completing these computations, comprising a new Cadabra module we call ``SusyPy.'' We provide a significant extension of the available tensor-arithmetic/canonicalization to include spinor-indexed expressions and NW-SE convention, and we provide a new Fierz expansion algorithm for spinor-indexed expressions. On top of this new tensor-spinor symbolic algebra, we have built algorithms for solving for the coefficients of a multiplet and its action, and for computing holoraumy, for both off-shell and on-shell N = 1 multiplets of any dimension. We apply our tools to assimilate linearized 11D, N = 1 supergravity into the Genomics project. We demonstrate solving the 11D, N = 1 multiplet, as in Cremmer, Julia, and Scherk, in a few lines of code, and we provide a comprehensive picture of the multiplet's non-closure geometry. Further, we provide the first-ever computation of the holoraumy of 11D, N = 1 supergravity. |
| title | Modern Tensor-Spinor Symbolic Algebra Algorithms and Computing Non-Closure Geometry & Holoraumy in 11D, N = 1 Supergravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2212.00614 |