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Title: Logarithmic singularities and maximally supersymmetric amplitudes

Abstract

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.more » 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.« less

Authors:
 [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
Publication Date:
Research Org.:
Univ. of California, Los Angeles, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1454795
Grant/Contract Number:  
SC0009937; SC0011632
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: 2015; Journal Issue: 6; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Extended Supersymmetry

Citation Formats

Bern, Zvi, Herrmann, Enrico, Litsey, Sean, Stankowicz, James, and Trnka, Jaroslav. Logarithmic singularities and maximally supersymmetric amplitudes. United States: N. p., 2015. Web. doi:10.1007/JHEP06(2015)202.
Bern, Zvi, Herrmann, Enrico, Litsey, Sean, Stankowicz, James, & Trnka, Jaroslav. Logarithmic singularities and maximally supersymmetric amplitudes. United States. doi:10.1007/JHEP06(2015)202.
Bern, Zvi, Herrmann, Enrico, Litsey, Sean, Stankowicz, James, and Trnka, Jaroslav. Tue . "Logarithmic singularities and maximally supersymmetric amplitudes". United States. doi:10.1007/JHEP06(2015)202. https://www.osti.gov/servlets/purl/1454795.
@article{osti_1454795,
title = {Logarithmic singularities and maximally supersymmetric amplitudes},
author = {Bern, Zvi and Herrmann, Enrico and Litsey, Sean and Stankowicz, James and Trnka, Jaroslav},
abstractNote = {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.},
doi = {10.1007/JHEP06(2015)202},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2015,
place = {United States},
year = {2015},
month = {6}
}

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