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Title: Computation of contour integrals on ℳ0,n
Authors: Cachazo, Freddy
Gomez, Humberto
Keywords: Differential and Algebraic Geometry
Scattering Amplitudes
Superstrings and Heterotic Strings
Issue Date: 1-Apr-2016
Publisher: Springer Verlag
Abstract: Contour integrals of rational functions over (Formula presented.) , the moduli space of n-punctured spheres, have recently appeared at the core of the tree-level S-matrix of massless particles in arbitrary dimensions. The contour is determined by the critical points of a certain Morse function on (Formula presented.). The integrand is a general rational function of the puncture locations with poles of arbitrary order as two punctures coincide. In this note we provide an algorithm for the analytic computation of any such integral. The algorithm uses three ingredients: an operation we call general KLT, Petersen’s theorem applied to the existence of a 2-factor in any 4-regular graph and Hamiltonian decompositions of certain 4-regular graphs. The procedure is iterative and reduces the computation of a general integral to that of simple building blocks. These are integrals which compute double-color-ordered partial amplitudes in a bi-adjoint cubic scalar theory. © 2016, The Author(s).
ISSN: 11266708
Appears in Collections:Artículos Científicos

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