The four-loop remainder function
Ancillary files for the paper
"The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory''
arXiv:1402.3300
by L. Dixon, J. Drummond, C. Duhr and J. Pennington

Symbol
  • The symbol of R64 has 1,544,205 terms, hence it is gzipped: R64symb.m.gz

    • Multiple Polylogarithms for Region I
  • The representation of R64 in Region I terms of multiple polylogarithms, or G functions,
    using the Lyndon basis defined in arXiv:1308.2276, has 746,773 terms, hence it is tar-gzipped: R64GRegionI.m.tar.gz
    [This is a single file, R64GRegionI.m, tar-gzipped instead of gzipped,
    in order to defeat "smart" browsers that want to uncompress the file for you.]

    • Coproduct Representation
  • The independent {5,1,1,1} coproduct components of R64, in terms of the weight-5 hexagon function basis in arXiv:1308.2276: R64_coproduct.m

    • Near collinear limit
  • The expansion of R64 in the near collinear limit, as a function of T, F and S, through order T^3 (gzipped): R64T3.m.gz

    • Near collinear/soft limits
  • The expansion of R64 in the near collinear limit, as a function of T, F and S, through order T^5, but also expanded around S=0: R64_TS
  • Same order T^5 expansion for the three-loop remainder function R63: R63_TS
  • Same order T^5 expansion for the two-loop remainder function R62: R62_TS
  • The advantage of these formulas is that all the harmonic polylogarithms (HPLs) are gone, there are only T, S, F, lnT = ln(T), lnS = ln(S), and the Riemann zeta values z2, z3, z4, z5, z6 and z7. And a lot of big rational numbers.

    • Multi-Regge limit
  • The NNLL BFKL eigenvalue E2.m and the NNNLL impact factor Phi3.m

  • The imaginary parts of R64 in the multi-Regge limit, the NNLL term (g_1^{(4)}) g41.m and the NNNLL term (g_0^{(4)}) g40.m

  • The NNLL term in the imaginary part of the five-loop remainder function R65 (g_2^{(5)}) g52.m

  • Similar files for the three-loop ratio function
  • and the four-loop ratio function