Abstract
We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar mathcal{N} = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.
Highlights
Have received considerable recent attention; see for example [6,7,8,9,10,11,12,13]
We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals
In the previous subsection we asked the amplituhedron directly to tell us which possible sets of cut conditions are valid for two-loop MHV amplitudes, rather than starting from some integral representation and using the amplituhedron to laboriously sift through the many spurious singularities
Summary
Have received considerable recent attention; see for example [6,7,8,9,10,11,12,13]. there remains a huge gap between our understanding of integrands and our understanding of the corresponding integrated amplitudes. Our goal in this paper is to improve greatly on the analysis of [17] We do this by presenting a method for asking the amplituhedron to directly provide a list of the physical branch points of a given amplitude. This is an inefficient approach, but armed with experience from that exercise we turn in section 3 to the development of a general, geometric algorithm for reading off the physical branch points of MHV amplitudes directly from the amplituhedron. Thanks to this implicit cyclic ordering we can usei as shorthand for the plane (i−1 i i+1), where indices are always understood to be mod n
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