An $N$-independent tensor decomposition for SU($N$)
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908474754990080 |
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| author | Keppeler, Stefan Sjodahl, Malin Telalovic, Bernanda |
| author_facet | Keppeler, Stefan Sjodahl, Malin Telalovic, Bernanda |
| contents | To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-$N$ decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An $N$-independent tensor decomposition for SU($N$) Keppeler, Stefan Sjodahl, Malin Telalovic, Bernanda High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Representation Theory 20C30, 81T10, 15A69, 20Cxx, 81R05 To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each irreducible representation by a pair of Young diagrams, with parts acting on quarks and antiquarks. By combining this with a column-wise multiplication of Young diagrams, we generalize the Littlewood-Richardson rule for the product of two Young diagrams to the product of two Young diagram pairs, achieving a general-$N$ decomposition. |
| title | An $N$-independent tensor decomposition for SU($N$) |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics Representation Theory 20C30, 81T10, 15A69, 20Cxx, 81R05 |
| url | https://arxiv.org/abs/2507.22981 |