Abstract
We calculate both at leading weak and strong coupling the renormalised Maldacena-Wilson loop for contours formed by consecutive passage of two touching circles. At the touching point both circles should have the same normal direction but form cusps of non-zero opening angle α. Particular emphasis is put on the behaviour in the limit α → 0 and its comparison with the spiky situation studied in a previous paper, where α was set to zero before renormalisation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.M. Polyakov, Gauge Fields as Rings of Glue, Nucl. Phys.B 164 (1980) 171 [INSPIRE].
R.A. Brandt, F. Neri and M.-a. Sato, Renormalization of Loop Functions for All Loops, Phys. Rev.D 24 (1981) 879 [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP01 (2016) 140 [arXiv:1510.07803] [INSPIRE].
J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett.80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J.C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
N. Drukker, D.J. Gross and H. Ooguri, Wilson loops and minimal surfaces, Phys. Rev.D 60 (1999) 125006 [hep-th/9904191] [INSPIRE].
H. Dorn, On a new type of divergence for spiky Wilson loops and related entanglement entropies, JHEP03 (2018) 124 [Erratum ibid.05 (2018) 108] [arXiv:1801.10367] [INSPIRE].
H. Dorn, On Wilson loops for two touching circles with opposite orientation, J. Phys.A 52 (2019) 095401 [arXiv:1811.00799] [INSPIRE].
P. Bueno, H. Casini and W. Witczak-Krempa, Generalizing the entanglement entropy of singular regions in conformal field theories, arXiv:1904.11495 [INSPIRE].
M. Ghasemi and S. Parvizi, Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime, arXiv:1905.01675 [INSPIRE].
D. Correa, P. Pisani, A. Rios Fukelman and K. Zarembo, Dyson equations for correlators of Wilson loops, JHEP12 (2018) 100 [arXiv:1811.03552] [INSPIRE].
H. Dorn, Wilson loops at strong coupling for curved contours with cusps, J. Phys.A 49 (2016) 145402 [arXiv:1509.00222] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys.B 826 (2010) 337 [arXiv:0712.1223] [INSPIRE].
M. Kruczenski, A Note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature, JHEP12 (2002) 024 [hep-th/0210115] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
N. Drukker and D.J. Gross, An Exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys.42 (2001) 2896 [hep-th/0010274] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys.313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1905.01101
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Dorn, H. More on Wilson loops for two touching circles. J. High Energ. Phys. 2019, 88 (2019). https://doi.org/10.1007/JHEP07(2019)088
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2019)088