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arXiv · 1512.08113

Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory

C. Vergu
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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.

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C. Vergu. 2015-12-26. Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory. https://arxiv.org/abs/1512.08113

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