Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills   We derive a set of first-order differential equations obeyed by the S-matrix
of planar maximally supersymmetric Yang-Mills theory. The equations, based on
the Yangian symmetry of the theory, involve only finite and
regulator-independent quantities and uniquely determine the all-loop S-matrix.
When expanded in powers of the coupling they give derivatives of amplitudes as
single integrals over lower-loop, higher-point amplitudes/Wilson loops. We
outline a derivation for the equations using the Operator Product Expansion for
Wilson loops. We apply them on a few examples at two- and three-loops,
reproducing a recent result on the two-loop NMHV hexagon and fixing previously
undermined coefficients in a recent Ansatz for the three-loop MHV hexagon. In
addition, we consider amplitudes restricted to a two-dimensional subspace of
Minkowski space and derive a particularly simple set of partially closed
equations in that case.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph