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J. D. Stasheff, “Homotopy Associativity of H-Spaces. I,” Transactions of the American Mathematical Society
1963
Earlier work this paper cites.
J. D. Stasheff, “Homotopy Associativity of H-Spaces. II,” Transactions of the American Mathematical Society
1963
Earlier work this paper cites.
R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP
Original
2007
Earlier work this paper cites.
J. M. Drummond and J. M. Henn, “All tree-level amplitudes in N=4 SYM,” JHEP
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges, and J. Trnka, “A Note on Polytopes for Scattering Amplitudes,” JHEP
Original
2012
Earlier work this paper cites.
A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP
Original
2013
Earlier work this paper cites.

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2018

An Etude on Recursion Relations and Triangulations

He, Song, Yang, Qinglin

Understand

Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint $\phi^3$ theory.

The recursion relies on properties of the amplitude that can be made manifest in the underlying kinematic associahedron, and it provides triangulations for the latter.
Furthermore, we solve the recursion relation and present all-multiplicity results for the amplitude: by reformulating the associahedron in terms of its vertices, it is given explicitly as a sum of "volume" of simplicies for any triangulation, which is an analogy of BCFW representation/triangulation of amplituhedron for ${\cal N}=4$ SYM.

Built on

J. D. Stasheff, “Homotopy Associativity of H-Spaces. I,” Transactions of the American Mathematical Society
1963
Earlier work this paper cites.
J. D. Stasheff, “Homotopy Associativity of H-Spaces. II,” Transactions of the American Mathematical Society
1963
Earlier work this paper cites.
R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys
2005
Earlier work this paper cites.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett
2005
Earlier work this paper cites.
N. Arkani-Hamed and J. Trnka, “The Amplituhedron,” JHEP
Original
2007
Earlier work this paper cites.
J. M. Drummond and J. M. Henn, “All tree-level amplitudes in N=4 SYM,” JHEP
Original
2009
Earlier work this paper cites.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. Hodges, and J. Trnka, “A Note on Polytopes for Scattering Amplitudes,” JHEP
Original
2012
Earlier work this paper cites.
A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP
Original
2013
Earlier work this paper cites.