Abstract
Motivated by reformulating Yangian invariants in planar \( \mathcal{N} \) = 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 \( \mathcal{A} \) 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.
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He, S., Li, Z. A note on letters of Yangian invariants. J. High Energ. Phys. 2021, 155 (2021). https://doi.org/10.1007/JHEP02(2021)155
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DOI: https://doi.org/10.1007/JHEP02(2021)155