Multi-loop positivity of the planar N = 4 SYM six-point amplitude

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Standard

Multi-loop positivity of the planar N = 4 SYM six-point amplitude. / Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.; Trnka, Jaroslav.

I: Journal of High Energy Physics, Bind 2017, Nr. 2, 112, 01.02.2017.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Dixon, LJ, von Hippel, M, McLeod, AJ & Trnka, J 2017, 'Multi-loop positivity of the planar N = 4 SYM six-point amplitude', Journal of High Energy Physics, bind 2017, nr. 2, 112. https://doi.org/10.1007/JHEP02(2017)112

APA

Dixon, L. J., von Hippel, M., McLeod, A. J., & Trnka, J. (2017). Multi-loop positivity of the planar N = 4 SYM six-point amplitude. Journal of High Energy Physics, 2017(2), [112]. https://doi.org/10.1007/JHEP02(2017)112

Vancouver

Dixon LJ, von Hippel M, McLeod AJ, Trnka J. Multi-loop positivity of the planar N = 4 SYM six-point amplitude. Journal of High Energy Physics. 2017 feb. 1;2017(2). 112. https://doi.org/10.1007/JHEP02(2017)112

Author

Dixon, Lance J. ; von Hippel, Matt ; McLeod, Andrew J. ; Trnka, Jaroslav. / Multi-loop positivity of the planar N = 4 SYM six-point amplitude. I: Journal of High Energy Physics. 2017 ; Bind 2017, Nr. 2.

Bibtex

@article{1bab55b05d1b40b79bf3c8922a28a59c,
title = "Multi-loop positivity of the planar N = 4 SYM six-point amplitude",
abstract = "We study the six-point NMHV ratio function in planar N = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a {"}radial{"} direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.",
keywords = "1/N Expansion, Scattering Amplitudes, Supersymmetric gauge theory",
author = "Dixon, {Lance J.} and {von Hippel}, Matt and McLeod, {Andrew J.} and Jaroslav Trnka",
year = "2017",
month = feb,
day = "1",
doi = "10.1007/JHEP02(2017)112",
language = "English",
volume = "2017",
journal = "Journal of High Energy Physics (Online)",
issn = "1126-6708",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Multi-loop positivity of the planar N = 4 SYM six-point amplitude

AU - Dixon, Lance J.

AU - von Hippel, Matt

AU - McLeod, Andrew J.

AU - Trnka, Jaroslav

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We study the six-point NMHV ratio function in planar N = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a "radial" direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.

AB - We study the six-point NMHV ratio function in planar N = 4 SYM theory in the context of positive geometry. The Amplituhedron construction of the integrand for the amplitudes provides a kinematical region in which the integrand was observed to be positive. It is natural to conjecture that this property survives integration, i.e. that the final result for the ratio function is also positive in this region. Establishing such a result would imply that preserving positivity is a surprising property of the Minkowski contour of integration and it might indicate some deeper underlying structure. We find that the ratio function is positive everywhere we have tested it, including analytic results for special kinematical regions at one and two loops, as well as robust numerical evidence through five loops. There is also evidence for not just positivity, but monotonicity in a "radial" direction. We also investigate positivity of the MHV six-gluon amplitude. While the remainder function ceases to be positive at four loops, the BDS-like normalized MHV amplitude appears to be positive through five loops.

KW - 1/N Expansion

KW - Scattering Amplitudes

KW - Supersymmetric gauge theory

U2 - 10.1007/JHEP02(2017)112

DO - 10.1007/JHEP02(2017)112

M3 - Journal article

VL - 2017

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 2

M1 - 112

ER -

ID: 279625400