TY - JOUR

T1 - Non-supersymmetric Wilson loop in N = 4 SYM and defect 1d CFT

AU - Beccaria, Matteo

AU - Giombi, Simone

AU - Tseytlin, Arkady A.

N1 - Funding Information:
We are grateful to L. Griguolo, C. Imbimbo, V. Pestun, R. Roiban, D. Seminara, D. Young and K. Zarembo for very useful discussions. The work of S.G. is supported in part by the US NSF under Grant No. PHY-1620542. AAT thanks KITP at UC Santa Barbara for hospitality while this work was in progress where his research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. He was also supported by STFC grant ST/P000762/1 and the Russian Science Foundation grant 14-42-00047 at Lebedev Institute.
Publisher Copyright:
© 2018, The Author(s).

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized Wilson loop operator containing a constant parameter ζ in front of the scalar coupling term, so that ζ = 0 corresponds to the standard Wilson loop, while ζ = 1 to the locally supersymmetric one. We compute the expectation value of this operator for circular loop as a function of ζ to second order in the planar weak coupling expansion in N = 4 SYM theory. We then explain the relation of the expansion near the two conformal points ζ = 0 and ζ = 1 to the correlators of scalar operators inserted on the loop. We also discuss the AdS5 × S5 string 1-loop correction to the strong-coupling expansion of the standard circular Wilson loop, as well as its generalization to the case of mixed boundary conditions on the five-sphere coordinates, corresponding to general ζ. From the point of view of the defect CFT1 defined on the Wilson line, the ζ-dependent term can be seen as a perturbation driving a RG flow from the standard Wilson loop in the UV to the supersymmetric Wilson loop in the IR. Both at weak and strong coupling we find that the logarithm of the expectation value of the standard Wilson loop for the circular contour is larger than that of the supersymmetric one, which appears to be in agreement with the 1d analog of the F-theorem.

AB - Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized Wilson loop operator containing a constant parameter ζ in front of the scalar coupling term, so that ζ = 0 corresponds to the standard Wilson loop, while ζ = 1 to the locally supersymmetric one. We compute the expectation value of this operator for circular loop as a function of ζ to second order in the planar weak coupling expansion in N = 4 SYM theory. We then explain the relation of the expansion near the two conformal points ζ = 0 and ζ = 1 to the correlators of scalar operators inserted on the loop. We also discuss the AdS5 × S5 string 1-loop correction to the strong-coupling expansion of the standard circular Wilson loop, as well as its generalization to the case of mixed boundary conditions on the five-sphere coordinates, corresponding to general ζ. From the point of view of the defect CFT1 defined on the Wilson line, the ζ-dependent term can be seen as a perturbation driving a RG flow from the standard Wilson loop in the UV to the supersymmetric Wilson loop in the IR. Both at weak and strong coupling we find that the logarithm of the expectation value of the standard Wilson loop for the circular contour is larger than that of the supersymmetric one, which appears to be in agreement with the 1d analog of the F-theorem.

KW - AdS-CFT Correspondence

KW - Supersymmetric Gauge Theory

KW - Wilson

KW - ’t Hooft and Polyakov loops

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U2 - 10.1007/JHEP03(2018)131

DO - 10.1007/JHEP03(2018)131

M3 - Article

AN - SCOPUS:85044518095

SN - 1126-6708

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 3

M1 - 131

ER -