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# Symmetric Wilson Loops beyond leading order

1 , 2 , 3

SciPost Physics

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### Abstract

We study the circular Wilson loop in the symmetric representation of in super-Yang-Mills (SYM). In the large limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests non-perturbative physics in the dual holographic theory. We also computed the next-to-leading order term in , and the result matches with the exact result from the -fundamental representation.

### Most cited references16

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### Localization of gauge theory on a four-sphere and supersymmetric Wilson loops

(2007)
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2 and the N=2* supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2 superconformal gauge theory is treated similarly.
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### Wilson Loops in N=4 Supersymmetric Yang--Mills Theory

(2000)
Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang-Mills theory are reported. For the two special cases of a circular loop and a pair of anti-parallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the results of the AdS/CFT correspondence, $$\sim\exp((constant)\sqrt{g^2N})$$. For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of $$\sqrt{g^2N}$$ also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order $$g^4N^2$$.
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### An Exact Prediction of N=4 SUSYM Theory for String Theory

(2000)
We propose that the expectation value of a circular BPS-Wilson loop in N=4 SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in alpha' and to all orders in g_s. We then compare this result with string theory. We find that the gauge theory calculation, for large g^2 N and to all orders in the 1/N^2 expansion does agree with the leading string theory calculation, to all orders in g_s and to lowest order in alpha'. We also find a relation between the expectation value of any closed smooth Wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity, and compare this result, again successfully, with string theory.
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### Author and article information

###### Affiliations
[1 ]Royal Institute of Technology (KTH)
[2 ]Stockholm University
[3 ]Uppsala University
###### Journal
SciPost Physics
SciPost Phys.
Stichting SciPost
2542-4653
2016
December 21 2016
: 1
: 2
10.21468/SciPostPhys.1.2.013