Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability

Abstract

We compute a set of correlation functions of operator insertions on the 1/8 BPS Wilson loop in $\mathcal{N}=4$ 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 AdS${}_2$ 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 some of their finite N generalizations. 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.

43+4 pages; v2 References added. Minor corrections. Explanation in section 4.2 expanded; v3 Corrected statements about nonplanar corrections

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• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Small deformations of supersymmetric Wilson loops and open spin-chains
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• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
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• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
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• A Semiclassical String Description of Wilson Loop with Local Operators
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory

Cited by in corpus (28)

• Bootstrapping the half-BPS line defect
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Line defects and radiation in $\mathcal{N}=2$ theories
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Broken global symmetries and defect conformal manifolds
• Handling Handles. Part II. Stratification and Data Analysis
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Topological Holography: The Example of The D2-D4 Brane System
• Spin chain integrability in non-supersymmetric Wilson loops
• Conformal dispersion relations for defects and boundaries
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• A review of the AdS/CFT Quantum Spectral Curve
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Observations on BPS observables in 6d
• Ladder Limit for Correlators of Wilson Loops
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Method of images in defect conformal field theories
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Interpolating Bremsstrahlung function in ABJM
• On analytical perturbative solution of ABJM quantum spectral curve
• Supersymmetric Wilson loops in two dimensions and duality
• Bethe ansatz inside Calogero-Sutherland models
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Separation of variables for higher rank integrable models: review of recent progress
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory