Yangian Symmetry of smooth Wilson Loops in $\mathcal{N} = $ 4 super Yang-Mills Theory

Müller, Dennis; Münkler, Hagen; Plefka, Jan; Pollok, Jonas; Zarembo, Konstantin

doi:10.1007/JHEP11(2013)081

Yangian Symmetry of smooth Wilson Loops in $\mathcal{N} =$ 4 super Yang-Mills Theory

Dennis Müller
(
- Humboldt U., Berlin
)
,
Hagen Münkler
(
- Humboldt U., Berlin
)
,
Jan Plefka
(
- Humboldt U., Berlin
)
,
Jonas Pollok
(
- Humboldt U., Berlin
)
,
Konstantin Zarembo
(
- Nordita and
- Royal Inst. Tech., Stockholm and
- Uppsala U. and
- Stockholm U.
)

Sep 6, 2013

35 pages

Published in:

JHEP 11 (2013) 081

Published: 2013

e-Print:

1309.1676 [hep-th]

DOI:

10.1007/JHEP11(2013)081

Report number:

HU-EP-13-42,
NORDITA-2013-64,
UUITP-10-13

View in:

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Abstract: (arXiv)

We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS_5 x S^5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the N=4 super Yang-Mills theory.

Note:

36 pages, 1 figure. v2: Typos corrected, version to be published in JHEP

Wilson
't Hooft and Polyakov loops
AdS-CFT Correspondence
Conformal and W Symmetry
supersymmetry: 4
symmetry: Yangian
gauge field theory: Yang-Mills
invariance: Yangian
symmetry: conformal
approximation: strong coupling

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Yangian Symmetry of smooth Wilson Loops in N=\mathcal{N} = N= 4 super Yang-Mills Theory

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Yangian Symmetry of smooth Wilson Loops in $\mathcal{N} =$ 4 super Yang-Mills Theory