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Exact correlators on the Wilson loop in $$$$ \mathcal{N}=4 $$$$ SYM: localization, defect CFT, and integrability

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Princeton Univ., NJ (United States). Dept. of Physics; Princeton Univ., NJ (United States)
  2. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
+ Show Author Affiliations

We compute a set of correlation functions of operator insertions on the 1/8 BPS Wilson loop in N=4 SYM by employing supersymmetric localization, OPE and the Gram-Schmidt orthogonalization. These correlators exhibit a simple determinant structure, are position-independent and form a topological subsector, but depend nontrivially on the ’t Hooft coupling and the rank of the gauge group. When applied to the 1/2 BPS circular (or straight) Wilson loop, our results provide an infinite family of exact defect CFT data, including the structure constants of protected defect primaries of arbitrary length inserted on the loop. At strong coupling, we show precise agreement with a direct calculation using perturbation theory around the AdS2 string worldsheet. We also explain the connection of our results to the “generalized Bremsstrahlung functions” previously computed from integrability techniques, reproducing the known results in the planar limit as well as obtaining their finite N generalization. Furthermore, we show that the correlators at large N can be recast as simple integrals of products of polynomials (known as Q-functions) that appear in the Quantum Spectral Curve approach. This suggests an interesting interplay between localization, defect CFT and integrability.

Research Organization:
Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0009988
OSTI ID:
1502487
Alternate ID(s):
OSTI ID: 22743046
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 5 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (7)

New compact construction of eigenstates for supersymmetric spin chains journal September 2018
Handling handles. Part II. Stratification and data analysis journal November 2018
More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve journal February 2019
Supersymmetric Wilson loops in two dimensions and duality journal July 2019
Line Defects and Radiation in N = 2 Conformal Theories journal October 2018
Handling handles. Part II. Stratification and data analysis text January 2018
Handling handles. Part II. Stratification and data analysis text January 2018

Figures / Tables (7)

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Figure 4(p. 34)figure Figure 4
Figure 5(p. 35)figure Figure 5
Figure 6(p. 36)figure Figure 6
Figure 7(p. 39)figure Figure 7

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT Correspondence
Conformal Field Theory
Supersymmetric Gauge Theory
Wilson
't Hooft and Polyakov loops