Yangian Symmetry for Bi-Scalar Loop Amplitudes

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

doi:10.1007/JHEP05(2018)003

Yangian Symmetry for Bi-Scalar Loop Amplitudes

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

Apr 6, 2017

40 pages

Published in:

JHEP 05 (2018) 003

Published: May 2, 2018

e-Print:

1704.01967 [hep-th]

DOI:

10.1007/JHEP05(2018)003

Report number:

HU-EP-17-09,
MITP-17-022,
LPTENS-17-07

View in:

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Abstract: (Springer)

We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ-twisted weakly coupled

\mathcal{N}=4

SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.

Note:

40 pages, 20 figures

Integrable Field Theories
AdS-CFT Correspondence
Conformal Field Theory
Quantum Groups
symmetry: Yangian
symmetry: conformal
supersymmetry: 4
operator: Lax
scattering amplitude
scalar particle

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