Scattering Amplitudes and Simple Canonical Forms for Simple Polytopes

Giulio Salvatori; Stefan Stanojevic

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arXiv · 1912.06125

Scattering Amplitudes and Simple Canonical Forms for Simple Polytopes

Giulio Salvatori·Stefan Stanojevic

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Abstract

We provide an efficient recursive formula to compute the canonical forms of arbitrary $d$-dimensional simple polytopes, which are convex polytopes such that every vertex lies precisely on $d$ facets. For illustration purposes, we explicitly derive recursive formulae for the canonical forms of Stokes polytopes, which play a similar role for a theory with quartic interaction as the Associahedron does in planar bi-adjoint $\phi^3$ theory. As a by-product, our formula also suggests a new way to obtain the full planar amplitude in $\phi^4$ theory by taking suitable limits of the canonical forms of constituent Stokes polytopes.

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Giulio Salvatori, Stefan Stanojevic. 2019-12-12. Scattering Amplitudes and Simple Canonical Forms for Simple Polytopes. https://arxiv.org/abs/1912.06125

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