Cluster patterns in Landau and leading singularities via the amplituhedron
Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 2, pp. 299-336.
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We advance the exploration of cluster-algebraic patterns in the building blocks of scattering amplitudes in 𝒩=4 super Yang–Mills theory. In particular, we conjecture that, given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding leading singularities can be found together in a cluster. We check these adjacencies for all one-loop amplitudes up to 9 points. Along the way, we also prove that all (rational) N2MHV Yangian invariants are cluster adjacent, confirming original conjectures.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/155
Classification : 70-XX, 13-XX
Mots-clés : Scattering amplitudes, cluster algebras, maximally supersymmetric Yang–Mills 
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     title = {Cluster patterns in {Landau} and leading singularities via the amplituhedron},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {299--336},
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     number = {2},
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     doi = {10.4171/aihpd/155},
     mrnumber = {4581445},
     zbl = {1515.70039},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpd/155/}
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Gürdoğan, Ömer; Parisi, Matteo. Cluster patterns in Landau and leading singularities via the amplituhedron. Annales de l’Institut Henri Poincaré D, Tome 10 (2023) no. 2, pp. 299-336. doi : 10.4171/aihpd/155. https://www.numdam.org/articles/10.4171/aihpd/155/
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  • Parisi, Matteo Cluster Algebras and Amplituhedra, Combinatorial Aspects of Scattering Amplitudes (2023), p. 157 | DOI:10.1007/978-3-031-41069-7_7
  • Parisi, Matteo; Sherman-Bennett, Melissa; Williams, Lauren The 𝑚=2 amplituhedron and the hypersimplex: Signs, clusters, tilings, Eulerian numbers, Communications of the American Mathematical Society, Volume 3 (2023) no. 7, p. 329 | DOI:10.1090/cams/23

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