Classical polylogarithms for amplitudes and Wilson loops.
By A. Goncharov, M. Spradlin, C. Vergu, A. Volovich. Physical Review Letters, 2010
663 citations recorded by the source corpus.
We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in N=4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Lik with cross ratios of momentum twistor invariants as their arguments. In deriving our formula we rely on results from the theory of motives.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/bfdb75e8c152ab0edb945ac29b7b6e99ac71fb07
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Citations in the corpus
- Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, neutral): “05 46”
- Hexagon functions and the three-loop remainder function (2013, background): “The two-loop remainder function R (2) 6 can be expressed simply in terms of classical polylogarithms [32].”
- Bootstrapping the three-loop hexagon (2011, methodology): “Not surprisingly, it contains the symbol of the two-loop remainder function which is explicitly known [35] and satisfies the above conditions.”
- Two-loop planar master integrals for Higgs → 3 partons with full heavy-quark mass dependence (2016, methodology): “We parametrize the two loop momenta using the spinor-helicity formalism [90] (see [91, 92] for a different formalism), k 1 = z1p μ 1 + z2p μ 2 + z3 〈1−|γμ|2−〉 2〈13〉[32] + z4 〈2−|γμ|1−〉 2〈23〉[31] , k 2 = z5p μ 1 + z6p μ 2 + z7 〈1−|γμ|2−〉 2〈13〉[32] + z8 〈2−|γμ|1−〉 2〈23〉[31] .”
- Scattering Amplitudes and the Positive Grassmannian (2012, methodology): “There has also been extraordinary progress in determining the amplitude itself beyond the integrand, using the technology of symbols of transcendental functions to powerfully constrain and control the polylogarithms occurring in the final results, [19, 20].”
- From polygons and symbols to polylogarithmic functions (2011, methodology): “ssible maximal dissections of a certain decorated polygon associated to the polylogarithm. In section 4 we give a short example of how to integrate a symbol following the approach introduced in refs. [60, 75], before generalizing this procedure to higher weights in section 5. In order to highlight r”
- Uniqueness of two-loop master contours (2012, neutral): “This enables us to obtain the symbols [59, 60] of each of the chiral double boxes.”
- Soft triple-real radiation for Higgs production at N3LO (2013, background): “and to define the symbol recursively by [122]”
- Motivic amplitudes and cluster coordinates (2013, methodology): “There is an invariant associated to any weight four function, with values in an Abelian group Λ2 B2, reviewed in section 4, which is the obstruction for the function to be expressible as a sum of products of classical polylogarithms Lim.”
- The four-loop six-gluon NMHV ratio function (2015, result): “The assumption that the functions lie in this space was originally inspired by the compact analytic form found for the two-loop remainder function [41], following earlier work [42, 43].”
- Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, methodology): “At two loops, we used the result of [12,51] for the two loops remainder function.”
- Bootstrapping an NMHV amplitude through three loops (2014, methodology): “Over the past two decades, calculations in planar N = 4 SYM have pushed further, in terms of loops, legs, and general understanding, than they have in other gauge theories [1–7].”
- Looking for a bulk point (2015, methodology): “In computations of perturbative correlators in scale-invariant theories, it has proven useful to introduce a “symbol” that captures some of the singularities of the integrals [14].”