Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM

Abstract

We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.

45 pages, 6 figures, ancillary Mathematica notebook; 1 figure added and minor changes in Appendix C

References in corpus (23)

• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Small deformations of supersymmetric Wilson loops and open spin-chains
• The Quantum Spectral Curve of the ABJM theory
• Localized magnetic field in the $O(N)$ model
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• A novel representation of an integrated correlator in $\mathcal{N}=4$ SYM theory
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• AdS Virasoro-Shapiro from single-valued periods
• AdS Virasoro-Shapiro from dispersive sum rules
• Towards the exact Bremsstrahlung function of ABJM theory
• Bootstrapping line defects with $O(2)$ global symmetry
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions
• Broken global symmetries and defect conformal manifolds
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory

Cited by in corpus (5)

• Conformal line defects at finite temperature
• Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Holographic Wilson Loop One-point Functions in ABJM Theory