More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve
Abstract
We perform here exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $$\mathcal{N}=4$$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $$Q$$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$$_2$$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. Specifically, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.
- Authors:
-
[2]
- Princeton Univ., NJ (United States). Dept. of Physics
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
- OSTI Identifier:
- 1596661
- Grant/Contract Number:
- SC0009988; PHY-1620542
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical
- Additional Journal Information:
- Journal Volume: 52; Journal Issue: 12; Journal ID: ISSN 1751-8113
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS/CFT; supersymmetry; conformal field theory; defect CFT
Citation Formats
Giombi, Simone, and Komatsu, Shota. More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve. United States: N. p., 2019.
Web. doi:10.1088/1751-8121/ab046c.
Giombi, Simone, & Komatsu, Shota. More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve. United States. https://doi.org/10.1088/1751-8121/ab046c
Giombi, Simone, and Komatsu, Shota. Mon .
"More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve". United States. https://doi.org/10.1088/1751-8121/ab046c. https://www.osti.gov/servlets/purl/1596661.
@article{osti_1596661,
title = {More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve},
author = {Giombi, Simone and Komatsu, Shota},
abstractNote = {We perform here exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $\mathcal{N}=4$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $Q$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$_2$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. Specifically, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.},
doi = {10.1088/1751-8121/ab046c},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 12,
volume = 52,
place = {United States},
year = {Mon Feb 25 00:00:00 EST 2019},
month = {Mon Feb 25 00:00:00 EST 2019}
}
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