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Title: Logarithmic singularities and maximally supersymmetric amplitudes

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [1];  [1];  [2]
  1. Univ. of California, Los Angeles, CA (United States). Dept. of Physics and Astronomy
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
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The dual formulation of planar N=4 super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity. Recently, Arkani-Hamed, Bourjaily, Cachazo and Trnka conjectured the same singularity properties hold to all loop orders in the nonplanar sector as well. Here we conjecture that to all loop orders these constraints give us the key integrand level analytic information contained in dual conformal symmetry. We also conjecture that to all loop orders, while N=8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. For the three-loop four-point N=4 super-Yang-Mills amplitude, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We then express the complete amplitude in terms of the basis diagrams, with the coefficients determined by unitarity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest via d log forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Furthermore, we present a variety of examples illustrating that these constraints are more restrictive than dual conformal symmetry. Our investigations show that the singularity structures of planar and nonplanar integrands in N=4 super-Yang-Mills are strikingly similar. While it is not clear how to extend either dual conformal symmetry or a dual formulation to the nonplanar sector, these results suggest that related concepts might exist and await discovery. Finally, we describe the singularity structure of N=8 supergravity at three loops and beyond.

Research Organization:
Univ. of California, Los Angeles, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0009937; SC0011632
OSTI ID:
1454795
Journal Information:
Journal of High Energy Physics (Online), Vol. 2015, Issue 6; 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

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From correlation functions to Wilson loops text January 2010
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Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data text January 2013
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ABJM amplitudes and the positive orthogonal grassmannian 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
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Anatomy of the Amplituhedron preprint January 2014
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Cited By (21)

All-loop cuts from the Amplituhedron journal April 2019
Two-loop $$ \mathcal{N} $$ = 2 SQCD amplitudes with external matter from iterated cuts journal July 2019
On-shell diagrams and the geometry of planar N < 4 $$ \mathcal{N}<4 $$ SYM theories journal November 2017
Positivity, Grassmannian geometry and simplex-like structures of scattering amplitudes journal December 2017
All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops journal March 2020
Top-forms of leading singularities in nonplanar multi-loop amplitudes journal February 2018
A planar four-loop form factor and cusp anomalous dimension in QCD text January 2016
The double pentaladder integral to all ordersC text January 2018
Evidence for a Nonplanar Amplituhedron text January 2015
Gravity On-shell Diagrams text January 2016
Full Colour for Loop Amplitudes in Yang-Mills Theory text January 2016
Prescriptive Unitarity text January 2017
Bootstrapping the QCD soft anomalous dimension text January 2017
The Sudakov form factor at four loops in maximal super Yang-Mills theory text January 2017
All-Helicity Symbol Alphabets from Unwound Amplituhedra text January 2017
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops text January 2017
The Double Pentaladder Integral to All Orders text January 2018
Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts text January 2018
The two-loop five-point amplitude in $\mathcal N=8$ supergravity text January 2019
All-loop cuts from the Amplituhedron text January 2019
Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops text January 2019

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Scattering Amplitudes
Extended Supersymmetry