From polygons and symbols to polylogarithmic functions

Duhr, Claude;Gangl, Herbert;Rhodes, John R.
(2012) Journal of High Energy Physics — Vol. 2012, n° 10, p. 75 (2012)

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Authors
  • Duhr, ClaudeUCLouvain
    Author
  • Gangl, Herbert
    Author
  • Rhodes, John R.
    Author
Abstract
We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple polylogarithm in terms of the combinatorial properties of an associated rooted decorated polygon. We also outline a systematic approach to constructing a function corresponding to a given symbol, and illustrate it in the particular case of harmonic polylogarithms up to weight four. Furthermore, part of the ambiguity of this process is highlighted by exhibiting a family of non-trivial elements in the kernel of the symbol map for arbitrary weight.
Affiliations
  • ETH ZurichInstitut für Theoretische Physik

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Duhr, C., Gangl, H., & Rhodes, J. R. (2012). From polygons and symbols to polylogarithmic functions. Journal of High Energy Physics, 2012(10), 75. https://doi.org/10.1007/JHEP10(2012)075 (Original work published 2012)