Partial flag cluster algebras reproduce a large part of the two-loop five- and six-point massless scattering symbol alphabets, with the momentum twistor embedding stronger at six points after permutation completion.
Partial flag varieties and preprojective algebras
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Let L be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories sub(Q) for Q an injective L-module, and we introduce a mutation operation between complete rigid modules in sub(Q). This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.
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Singularities of massless scattering and cluster algebras
Partial flag cluster algebras reproduce a large part of the two-loop five- and six-point massless scattering symbol alphabets, with the momentum twistor embedding stronger at six points after permutation completion.