Yangian Symmetry for Fishnet Feynman Graphs

Chicherin, Dmitry; Kazakov, Vladimir; Loebbert, Florian; Müller, Dennis; Zhong, De-liang

doi:10.1103/PhysRevD.96.121901

Yangian Symmetry for Fishnet Feynman Graphs

Dmitry Chicherin
(
- U. Mainz, PRISMA
)
,
Vladimir Kazakov
(
- Ecole Normale Superieure
)
,
Florian Loebbert
(
- Humboldt U., Berlin and
- Santa Barbara, KITP
)
,
Dennis Müller
(
- Humboldt U., Berlin and
- Santa Barbara, KITP
)
,
De-liang Zhong
(
- Ecole Normale Superieure
)

Jul 31, 2017

6 pages

Published in:

Phys.Rev.D 96 (2017) 12, 121901

Published: Dec 22, 2017

e-Print:

1708.00007 [hep-th]

DOI:

10.1103/PhysRevD.96.121901

Report number:

MITP-17-049,
HU-EP-17-20,
LPTENS-17-32

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Abstract: (APS)

Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double-scaling limits of planar, γ-twisted N=4 super Yang–Mills or Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the planar AdS/CFT correspondence.

Note:

6 pages, 5 figures

symmetry: Yangian
dimension: 4
supersymmetry: 4
space-time: dimension: 6
algebra: conformal
field theory: conformal
Feynman graph
AdS/CFT correspondence
differential equations
scattering amplitude

References(21)

Figures(12)

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,
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(
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)
,
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to be published

D. Chicherin
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V. Kazakov
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F. Loebbert
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D. Müller
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D.-l. Zhong

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