Abstract
We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.
Highlights
We conjecture a new set of analytic relations for scattering amplitudes in planar N 1⁄4 4 super Yang-Mills theory
Cluster algebras: There is evidence [1] that cluster algebras [18,19,20] address the question of which set of letters φi, called the alphabet, appear in the symbol of certain scattering amplitudes in planar N 1⁄4 4 super YangMills theory
A Grð4; nÞ cluster algebra consists of clusters that are represented by quiver diagrams of nodes connected by arrows and carry the A coordinates, which are the letters potentially appearing in the symbol of the n-particle scattering amplitude
Summary
We conjecture a new set of analytic relations for scattering amplitudes in planar N 1⁄4 4 super Yang-Mills theory. Cluster algebras: There is evidence [1] that cluster algebras [18,19,20] address the question of which set of letters φi, called the alphabet, appear in the symbol of certain scattering amplitudes in planar N 1⁄4 4 super YangMills theory. A Grð4; nÞ cluster algebra consists of clusters that are represented by quiver diagrams of nodes connected by arrows and carry the A coordinates, which are the letters potentially appearing in the symbol of the n-particle scattering amplitude.
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