A note on letters of Yangian invariants
Abstract Motivated by reformulating Yangian invariants in planar N $$ \mathcal{N} $$ = 4 SYM directly as d log forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the d log’s, which we call “letters”, for any Yangian invariant. These are functions o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2021)155 |
| _version_ | 1819297950569857024 |
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| author | Song He Zhenjie Li |
| author_facet | Song He Zhenjie Li |
| author_sort | Song He |
| collection | DOAJ |
| description | Abstract Motivated by reformulating Yangian invariants in planar N $$ \mathcal{N} $$ = 4 SYM directly as d log forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the d log’s, which we call “letters”, for any Yangian invariant. These are functions of momentum twistors Z ’s, given by the positive coordinates α’s of parametrizations of the matrix C(α), evaluated on the support of polynomial equations C(α) · Z = 0. We provide evidence that the letters of Yangian invariants are related to the cluster algebra of Grassmannian G(4, n), which is relevant for the symbol alphabet of n-point scattering amplitudes. For n = 6, 7, the collection of letters for all Yangian invariants contains the cluster A $$ \mathcal{A} $$ coordinates of G(4, n). We determine algebraic letters of Yangian invariant associated with any “four-mass” box, which for n = 8 reproduce the 18 multiplicative-independent, algebraic symbol letters discovered recently for two-loop amplitudes. |
| first_indexed | 2024-12-24T05:22:09Z |
| format | Article |
| id | doaj.art-2058b6504cf24ab6ad5cb141326a5b48 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-24T05:22:09Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2058b6504cf24ab6ad5cb141326a5b482022-12-21T17:13:27ZengSpringerOpenJournal of High Energy Physics1029-84792021-02-012021211510.1007/JHEP02(2021)155A note on letters of Yangian invariantsSong He0Zhenjie Li1CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesCAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesAbstract Motivated by reformulating Yangian invariants in planar N $$ \mathcal{N} $$ = 4 SYM directly as d log forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments of the d log’s, which we call “letters”, for any Yangian invariant. These are functions of momentum twistors Z ’s, given by the positive coordinates α’s of parametrizations of the matrix C(α), evaluated on the support of polynomial equations C(α) · Z = 0. We provide evidence that the letters of Yangian invariants are related to the cluster algebra of Grassmannian G(4, n), which is relevant for the symbol alphabet of n-point scattering amplitudes. For n = 6, 7, the collection of letters for all Yangian invariants contains the cluster A $$ \mathcal{A} $$ coordinates of G(4, n). We determine algebraic letters of Yangian invariant associated with any “four-mass” box, which for n = 8 reproduce the 18 multiplicative-independent, algebraic symbol letters discovered recently for two-loop amplitudes.https://doi.org/10.1007/JHEP02(2021)155Scattering AmplitudesSupersymmetric Gauge Theory |
| spellingShingle | Song He Zhenjie Li A note on letters of Yangian invariants Journal of High Energy Physics Scattering Amplitudes Supersymmetric Gauge Theory |
| title | A note on letters of Yangian invariants |
| title_full | A note on letters of Yangian invariants |
| title_fullStr | A note on letters of Yangian invariants |
| title_full_unstemmed | A note on letters of Yangian invariants |
| title_short | A note on letters of Yangian invariants |
| title_sort | note on letters of yangian invariants |
| topic | Scattering Amplitudes Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP02(2021)155 |
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