Abstract
Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the \( \mathcal{N} \) = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
A.M. Polyakov, Gauge Fields as Rings of Glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
V.S. Dotsenko and S.N. Vergeles, Renormalizability of Phase Factors in the NonAbelian Gauge Theory, Nucl. Phys. B 169 (1980) 527 [INSPIRE].
J.-L. Gervais and A. Neveu, The Slope of the Leading Regge Trajectory in Quantum Chromodynamics, Nucl. Phys. B 163 (1980) 189 [INSPIRE].
I.Y. Arefeva, Quantum contour field equations, Phys. Lett. B 93 (1980) 347 [INSPIRE].
H. Dorn, Renormalization of Path Ordered Phase Factors and Related Hadron Operators in Gauge Field Theories, Fortsch. Phys. 34 (1986) 11 [INSPIRE].
R.M. Marinho and L. Boanerges Peixoto, Charge renormalization of the Yang-Mills theory up to fourth order using dimensional regularization, Nuovo Cim. A 97 (1987) 148 [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].
J. Polchinski and J. Sully, Wilson Loop Renormalization Group Flows, JHEP 10 (2011) 059 [arXiv:1104.5077] [INSPIRE].
M. Beccaria, S. Giombi and A. Tseytlin, Non-supersymmetric Wilson loop in \( \mathcal{N} \) = 4 SYM and defect 1d CFT, JHEP 03 (2018) 131 [arXiv:1712.06874] [INSPIRE].
M. Beccaria and A.A. Tseytlin, On non-supersymmetric generalizations of the Wilson-Maldacena loops in N = 4 SYM, Nucl. Phys. B 934 (2018) 466 [arXiv:1804.02179] [INSPIRE].
M. Cooke, A. Dekel and N. Drukker, The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines, J. Phys. A 50 (2017) 335401 [arXiv:1703.03812] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Correlators on non-supersymmetric Wilson line in \( \mathcal{N} \) = 4 SYM and AdS2/CFT1, JHEP 05 (2019) 122 [arXiv:1903.04365] [INSPIRE].
D.H. Correa, V.I. Giraldo-Rivera and G.A. Silva, Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations, JHEP 03 (2020) 010 [arXiv:1910.04225] [INSPIRE].
N.B. Agmon and Y. Wang, Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines, arXiv:2009.06650 [INSPIRE].
G. Cuomo, Z. Komargodski and A. Raviv-Moshe, Renormalization Group Flows on Line Defects, arXiv:2108.01117 [INSPIRE].
R.A. Brandt, F. Neri and M.-a. Sato, Renormalization of Loop Functions for All Loops, Phys. Rev. D 24 (1981) 879 [INSPIRE].
C. Hoyos, A defect action for Wilson loops, JHEP 07 (2018) 045 [arXiv:1803.09809] [INSPIRE].
I.R. Klebanov, S.S. Pufu and B.R. Safdi, F-Theorem without Supersymmetry, JHEP 10 (2011) 038 [arXiv:1105.4598] [INSPIRE].
S. Giombi and I.R. Klebanov, Interpolating between a and F, JHEP 03 (2015) 117 [arXiv:1409.1937] [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Generalized F -Theorem and the ϵ Expansion, JHEP 12 (2015) 155 [arXiv:1507.01960] [INSPIRE].
N. Kobayashi, T. Nishioka, Y. Sato and K. Watanabe, Towards a C -theorem in defect CFT, JHEP 01 (2019) 039 [arXiv:1810.06995] [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
D. Friedan and A. Konechny, On the boundary entropy of one-dimensional quantum systems at low temperature, Phys. Rev. Lett. 93 (2004) 030402 [hep-th/0312197] [INSPIRE].
R. Brüser, S. Caron-Huot and J.M. Henn, Subleading Regge limit from a soft anomalous dimension, JHEP 04 (2018) 047 [arXiv:1802.02524] [INSPIRE].
D. Grabner, N. Gromov and J. Julius, Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve, JHEP 07 (2020) 042 [arXiv:2001.11039] [INSPIRE].
P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 104 (2021) L081703 [arXiv:2103.10440] [INSPIRE].
J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [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].
D. Correa, P. Pisani, A. Rios Fukelman and K. Zarembo, Dyson equations for correlators of Wilson loops, JHEP 12 (2018) 100 [arXiv:1811.03552] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2110.04212
Also at the Institute for Theoretical and Mathematical Physics (ITMP) of Moscow University and Lebedev Institute. (A. A. Tseytlin)
Rights and permissions
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.
About this article
Cite this article
Beccaria, M., Giombi, S. & Tseytlin, A.A. Higher order RG flow on the Wilson line in \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2022, 56 (2022). https://doi.org/10.1007/JHEP01(2022)056
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2022)056