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Title: The double pentaladder integral to all orders

Journal Article · · Journal of High Energy Physics (Online)
 [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)
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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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-76SF00515
OSTI ID:
1468694
Report Number(s):
SLAC-PUB--17228; PII: 8707
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Bootstrapping the three-loop hexagon text January 2011
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Cited By (19)

Cluster algebras and the subalgebra constructibility of the seven-particle remainder function journal January 2019
Perturbative four-point functions in planar N = 4 $$ \mathcal{N}=4 $$ SYM From hexagonalization journal January 2019
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case journal January 2019
Multipoint conformal blocks in the comb channel journal February 2019
Cluster adjacency and the four-loop NMHV heptagon journal March 2019
The Sklyanin bracket and cluster adjacency at all multiplicity journal March 2019
Rationalizing loop integration journal August 2018
Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM journal October 2018
Prescriptive unitarity for non-planar six-particle amplitudes at two loops journal December 2019
Bounded Collection of Feynman Integral Calabi-Yau Geometries journal January 2019
Cluster adjacency and the four-loop NMHV heptagon text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2019
Rationalizing Loop Integration text January 2018
Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function text January 2018
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case text January 2018
Cluster adjacency and the four-loop NMHV heptagon text January 2018
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity text January 2019
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case text January 2019

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