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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), Vol. 2018, Issue 7; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 48 works
Citation information provided by
Web of Science

References (133)

Heptagons from the Steinmann cluster bootstrap journal February 2017
Supersymmetry, supergravity theories and the dual spinor model journal April 1977
Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory journal January 2012
Gluing Ladder Feynman Diagrams into Fishnets journal August 2017
The Amplituhedron journal October 2014
Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills journal May 1997
Galois symmetries of fundamental groupoids and noncommutative geometry journal June 2005
Grassmannian Geometry of Scattering Amplitudes book May 2016
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes journal August 2012
Local spacetime physics from the Grassmannian journal January 2011
Evidence for a nonplanar amplituhedron journal June 2016
Magic identities for conformal four-point integrals journal January 2007
Into the amplituhedron journal December 2014
Hexagon OPE resummation and multi-Regge kinematics journal February 2016
Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory conference August 2014
Evaluating the six-point remainder function near the collinear limit journal October 2014
The four-loop six-gluon NMHV ratio function journal January 2016
Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal August 2010
Spacetime and Flux Tube S -Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory journal August 2013
Nested sums, expansion of transcendental functions, and multiscale multiloop integrals journal June 2002
Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory journal March 2010
The massless hexagon integral in D=6 dimensions journal September 2011
From d logs to dilogs; the super Yang-Mills MHV amplitude revisited journal January 2014
Supersymmetric Yang-Mills theories journal March 1977
Bootstrapping pentagon functions journal May 2018
New differential equations for on-shell loop integrals journal April 2011
Cluster Adjacency Properties of Scattering Amplitudes in N = 4 Supersymmetric Yang-Mills Theory journal April 2018
Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$ journal January 2009
OPE for all helicity amplitudes journal August 2015
First Look at Two-Loop Five-Gluon Scattering in QCD journal March 2018
Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion journal September 2014
Uniqueness of two-loop master contours journal October 2012
Pulling the straps of polygons journal December 2011
Real-virtual contributions to the inclusive Higgs cross-section at N3LO journal December 2013
Exact results for three- and four-point ladder diagrams with an arbitrary number of rungs journal May 1993
Superstring amplitudes and the associator journal August 2013
Leading singularities and off-shell conformal integrals journal August 2013
Hexagon Wilson loop OPE and harmonic polylogarithms journal November 2013
Polylogarithmes multiples uniformes en une variable journal April 2004
Mellin amplitudes for dual conformal integrals journal August 2012
Conformal properties of four-gluon planar amplitudes and Wilson loops journal May 2008
Bootstrapping an NMHV amplitude through three loops journal October 2014
The Galois coaction on $\phi^4$ periods journal January 2017
Hexagon functions and the three-loop remainder function journal December 2013
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations journal December 2016
Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms journal March 2018
Feynman amplitudes, coaction principle, and cosmic Galois group journal January 2017
New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level journal April 2017
Review of AdS/CFT Integrability: An Overview journal October 2011
Gluon scattering amplitudes at strong coupling journal June 2007
A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon journal March 2015
Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes journal May 2017
Bootstrapping the three-loop hexagon journal November 2011
On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences journal October 1998
Eliminating spurious poles from gauge-theoretic amplitudes journal May 2013
Azurite : An algebraic geometry based package for finding bases of loop integrals journal December 2017
Leading singularities and off-shell conformal integrals text January 2013
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in $ \mathcal{N} = 4 $ SYM journal June 2011
Dual superconformal invariance, momentum twistors and Grassmannians journal November 2009
Logarithmic singularities and maximally supersymmetric amplitudes journal June 2015
The Galois coaction on the electron anomalous magnetic moment journal January 2018
Harmonic Polylogarithms journal February 2000
Motivic amplitudes and cluster coordinates journal January 2014
Hexagonalization of correlation functions journal January 2017
Optical theorems and steinmann relations journal April 1975
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM journal January 2011
A duality for the S matrix journal March 2010
The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops journal March 2012
Exponential suppression with four legs and an infinity of loops journal August 2010
Thermodynamic bubble ansatz journal September 2011
Uniform asymptotic expansions for hypergeometric functions with large parameters IV journal October 2014
Generalised Ladders and Single-valued Polylogs text January 2012
From the holomorphic Wilson loop to ‘d log’ loop-integrands of super-Yang-Mills amplitudes journal May 2013
Classical Polylogarithms for Amplitudes and Wilson Loops journal October 2010
Multi-loop Feynman integrals and conformal quantum mechanics journal July 2003
Heptagons from the Steinmann Cluster Bootstrap text January 2017
Hexagonal Wilson loops in planar ${ \mathcal N }=4$ SYM theory at finite coupling journal September 2016
From polygons and symbols to polylogarithmic functions journal October 2012
Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism journal May 2018
Graphical functions and single-valued multiple polylogarithms journal January 2014
Generalised ladders and single-valued polylogs journal February 2013
The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory journal June 2014
Local integrals for planar scattering amplitudes journal June 2012
Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction journal July 2017
Symbolic expansion of transcendental functions journal June 2002
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data journal January 2014
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions journal August 2014
OPE for all helicity amplitudes II. Form factors and data analysis journal December 2015
Mathematical Aspects of Scattering Amplitudes conference November 2015
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes text January 2012
Motivic amplitudes and cluster coordinates text January 2014
Eliminating spurious poles from gauge-theoretic amplitudes preprint January 2009
Dual Superconformal Invariance, Momentum Twistors and Grassmannians text January 2009
Local Spacetime Physics from the Grassmannian text January 2009
Classical Polylogarithms for Amplitudes and Wilson Loops text January 2010
Review of AdS/CFT Integrability: An Overview text January 2010
Pulling the straps of polygons text January 2011
The massless hexagon integral in D = 6 dimensions text January 2011
The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM text January 2011
Bootstrapping the three-loop hexagon text January 2011
From polygons and symbols to polylogarithmic functions text January 2011
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory text January 2011
Hepta-Cuts of Two-Loop Scattering Amplitudes text January 2012
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes text January 2012
Mellin Amplitudes for Dual Conformal Integrals text January 2012
Uniqueness of two-loop master contours text January 2012
Superstring amplitudes and the associator text January 2013
Graphical functions and single-valued multiple polylogarithms preprint January 2013
Leading singularities and off-shell conformal integrals text January 2013
Hexagon Wilson Loop OPE and Harmonic Polylogarithms text January 2013
Real-Virtual contributions to the inclusive Higgs cross-section at N3LO text January 2013
The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory text January 2014
Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory preprint January 2014
Bootstrapping an NMHV amplitude through three loops text January 2014
OPE for all Helicity Amplitudes text January 2014
Logarithmic Singularities and Maximally Supersymmetric Amplitudes preprint January 2014
A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory text January 2015
Evidence for a Nonplanar Amplituhedron text January 2015
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations text January 2016
Hexagonalization of Correlation Functions text January 2016
Heptagons from the Steinmann Cluster Bootstrap text January 2016
The algebraic structure of cut Feynman integrals and the diagrammatic coaction text January 2017
A first look at two-loop five-gluon scattering in QCD text January 2017
Harmonic Polylogarithms text January 1999
Multi-loop Feynman integrals and conformal quantum mechanics text January 2003
On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences text January 1998
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory journal October 2015
Azurite : An algebraic geometry based package for finding bases of loop integrals journal December 2017
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory text January 2008
Towards a Basis for Planar Two-Loop Integrals text January 2010
Two-Loop Maximal Unitarity with External Masses text January 2012
Subleading Poles in the Numerical Unitarity Method at Two Loops text January 2017
On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences text January 1998

Cited By (10)

Cluster adjacency and the four-loop NMHV heptagon text January 2019
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case journal January 2019
Cluster adjacency and the four-loop NMHV heptagon text January 2018
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case 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

Figures / Tables (7)

Figure 1(p. 9)figure Figure 1
Figure 2(p. 10)figure Figure 2
Figure 3(p. 12)figure Figure 3
Table 1(p. 40)table Table 1
Table 2(p. 51)table Table 2
Table 3(p. 52)table Table 3
Table 4(p. 53)table Table 4

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Scattering Amplitudes
Nonperturbative Effects
1/N Expansion
Conformal and W Symmetry