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2018

Stokes Polytopes : The positive geometry for $\phi^{4}$ interactions

Banerjee, Pinaki, Laddha, Alok, Raman, Prashanth

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In a remarkable recent work [arXiv : 1711.09102] by Arkani-Hamed et al, the amplituhedron program was extended to the realm of non-supersymmetric scattering amplitudes.

In particular it was shown that for tree-level planar diagrams in massless $\phi^{3}$ theory (and its close cousin, bi-adjoint $\phi^{3}$ theory) a polytope known as the associahedron sits inside the kinematic space and is the amplituhedron for the theory.
Precisely as in the case of amplituhedron, it was shown that scattering amplitude is nothing but residue of the canonical form associated to the associahedron.
Combinatorial and geometric properties of associahedron naturally encode properties like locality and unitarity of (tree level) scattering amplitudes.

Stokes Polytopes : The positive geometry for $\phi^{4}$ interactions · Around

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A. Padrol, Y. Palu, V. Pilaud, and P.-G. Plamondon, Associahedra for finite type cluster algebras and minimal relations between 𝐠 \mathbf{g} -vectors
Original
1906
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J. D. Stasheff, Homotopy associativity of h-spaces. i
1963
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J. D. Stasheff, Homotopy associativity of h-spaces. ii
1963
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P. DELIGNE and D. MUMFORD, The irreducibility of the space of curves of given genus
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Y. Baryshnikov, On stokes sets
2001
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R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory
2005
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