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Algebraic singularities of scattering amplitudes from tropical geometry

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arxiv 1912.08217 v1 pith:7QJG3ONR submitted 2019-12-17 hep-th

Algebraic singularities of scattering amplitudes from tropical geometry

James Drummond , Jack Foster , \"Omer G\"urdo\u{g}an , Chrysostomos Kalousios This is my paper
classification hep-th
keywords amplitudesfinitelettersscatteringtropicalalgebraicalgebrasalphabet
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $\mathcal{N}=4$ super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

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Cited by 3 Pith papers

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  1. QCD Scattering Amplitudes and Prescriptive Unitarity

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    The maximally-transcendental part of planar two-loop six-gluon MHV QCD amplitudes is bootstrapped at symbol level and expressed in a 137-letter alphabet.

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    hep-th 2021-12 unverdicted novelty 7.0

    Cluster algebras for planar conformal kinematics are identified as G(4,n) subalgebras and used to bootstrap the symbol of an 8-point three-loop wheel integral via D3 and new algebraic letters.

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    hep-th 2026-03 conditional novelty 6.0

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