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Title: The double pentaladder integral to all orders

Abstract

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 = 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. Here in this paper, 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.

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [5]
  1. McGill Univ., Montreal, QC (Canada). Dept of Physics
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Ecole Normale Superieure, Paris (France). Lab. de Physique Theorique
  3. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Niels Bohr International Academy, Copenhagen (Denmark)
  4. SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Niels Bohr International Academy, Copenhagen (Denmark)
  5. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1468694
Report Number(s):
SLAC-PUB-17228
Journal ID: ISSN 1029-8479; PII: 8707
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Scattering Amplitudes; Nonperturbative Effects; 1/N Expansion; Conformal and W Symmetry

Citation Formats

Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., and Papathanasiou, Georgios. The double pentaladder integral to all orders. United States: N. p., 2018. Web. doi:10.1007/jhep07(2018)170.
Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., & Papathanasiou, Georgios. The double pentaladder integral to all orders. United States. https://doi.org/10.1007/jhep07(2018)170
Caron-Huot, Simon, Dixon, Lance J., von Hippel, Matt, McLeod, Andrew J., and Papathanasiou, Georgios. Fri . "The double pentaladder integral to all orders". United States. https://doi.org/10.1007/jhep07(2018)170. https://www.osti.gov/servlets/purl/1468694.
@article{osti_1468694,
title = {The double pentaladder integral to all orders},
author = {Caron-Huot, Simon and Dixon, Lance J. and von Hippel, Matt and McLeod, Andrew J. and Papathanasiou, Georgios},
abstractNote = {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 = 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. Here in this paper, 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.},
doi = {10.1007/jhep07(2018)170},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2018,
place = {United States},
year = {2018},
month = {7}
}

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Figures / Tables:

Figure 1 Figure 1: The eight- or higher-point $L$-loop ladder integral, labelled by dual coordinates.

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Bootstrapping the three-loop hexagon
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From polygons and symbols to polylogarithmic functions
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Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
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Hepta-Cuts of Two-Loop Scattering Amplitudes
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Mellin Amplitudes for Dual Conformal Integrals
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Uniqueness of two-loop master contours
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Superstring amplitudes and the associator
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Leading singularities and off-shell conformal integrals
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Hexagon Wilson Loop OPE and Harmonic Polylogarithms
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Real-Virtual contributions to the inclusive Higgs cross-section at N3LO
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Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory
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Bootstrapping an NMHV amplitude through three loops
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.