Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
arXiv:1512.08113
Abstract
Scattering amplitudes in N = 4 super-Yang Mills theory can be computed to higher perturbative orders than in any other four-dimensional quantum field theory. The results are interesting transcendental functions. By a hidden symmetry (dual conformal symmetry) the arguments of these functions have a geometric interpretation in terms of configurations of points in CP^3 and they turn out to be cluster coordinates. We briefly introduce cluster algebras and discuss their Poisson structure and the Sklyanin bracket. Finally, we present a 40-term trilogarithm identity which was discovered by accident while studying the physical results.
Expanded version of a talk given at the Opening Workshop of the Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory, organized by José I. Burgos Gil, Kurusch Ebrahimi-Fard, D. Ellwood, Ulf Kühn, Dominique Manchon and P. Tempesta. To be published in the conference proceedings
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