2018/06/30 by Simon Caron-Huot, Lance J. Dixon, Matt von Hippel +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Conformal map #Elliptic integral #Function (biology) #Hypergeometric distribution #Hypergeometric function #Invariant (physics) #Mathematical functions and polynomials #Multiple integral #Planar #Space (punctuation) #hep-th
paper · pdf · doi:10.1007/jhep07(2018)170
70 pages, 3 figures, 4 tables; v2, minor typo corrections and clarifications
openalex created_date 2018/06/13 · openalex publication_date 2018/07/01 · arxiv created 2018/07/26 · arxiv updated 2018/08/15 · openalex updated_date 2026/08/06
A bstract We compute dual-conformally invariant ladder integrals that are capped off by pentagons at each end of the ladder. Such integrals appear in six-point amplitudes in planar N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super-Yang-Mills theory. We provide exact, finite-coupling formulas for the basic double pentaladder integrals as a single Mellin integral over hypergeometric functions. For particular choices of the dual conformal cross ratios, we can evaluate the integral at weak coupling to high loop orders in terms of multiple polylogarithms. We argue that the integrals are exponentially suppressed at strong coupling. We describe the space of functions that contains all such double pentaladder integrals and their derivatives, or coproducts. This space, a prototype for the space of Steinmann hexagon functions, has a simple algebraic structure, which we elucidate by considering a particular discontinuity of the functions that localizes the Mellin integral and collapses the relevant symbol alphabet. This function space is endowed with a coaction, both perturbatively and at finite coupling, which mixes the independent solutions of the hypergeometric differential equation and constructively realizes a coaction principle of the type believed to hold in the full Steinmann hexagon function space.