Scattering Amplitudes from Intersection Theory

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We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated with a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann spheres, intersection numbers become tree-level scattering amplitudes of quantum field theories in the Cachazo-He-Yuan formulation.

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Sebastian Mizera

Princeton University

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Physical Review Letters

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University of Waterloo

Perimeter Institute

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Sebastian Mizera (Fri,) studied this question.

synapsesocial.com/papers/69dcc8ba89c4deb67d359f2c — DOI: https://doi.org/10.1103/physrevlett.120.141602

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Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Proof of the formula of Cachazo, He and Yuan for Yang-Mills tree amplitudes in arbitrary dimension· 2014 · 116 citations
Hypergeometric Functions, My Love· 1997 · 155 citations
Hypergeometric functions, my love : modular interpretations of configuration spaces· 1997 · 28 citations
Homotopy Invariant Algebraic Structures· 1999 · 47 citations
Perturbative Gauge Theory As A String Theory In Twistor Space· 2003 · 985 citations

Scattering Amplitudes from Intersection Theory

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