Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM

Abstract

We study the correlators of a recently discovered family of BPS Wilson loops in $\mathcal{N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant $g$ and for any rank $N$, by exploiting the suspected relation with two-dimensional gauge theories. We check this formula perturbatively at order $\mathcal{O}(g^4)$ for two latitude Wilson loops and we show that, in the limit where one of the loops shrinks to a point, logarithmic corrections in the shrinking radius are absent at $\mathcal{O}(g^6)$. This last result strongly supports the validity of our general expression and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop. At strong coupling we compare our result to the string dual of the $\mathcal{N}=4$ SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.

20 page, 8 figures

References in corpus (27)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Two Dimensional Gauge Theories Revisited
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• Magic identities for conformal four-point integrals
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
• Supersymmetric Wilson loops on S^3
• On N=8 Supergravity on $Ad{S}_5$ and N=4 Superconformal Yang-Mills theory
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
• More supersymmetric Wilson loops
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• More exact predictions of SUSYM for string theory
• Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
• Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription
• Wavy Wilson Line and AdS/CFT
• Supersymmetric Wilson loops at two loops
• Operator product expansion of higher rank Wilson loops from D-branes and matrix models
• Antisymmetric tensor field on $Ad{S}_5$
• BPS Wilson Loops on S^2 at Higher Loops
• Comparing strings in AdS(5)xS(5) to planar diagrams: an example
• Exact 1/4 BPS Loop - Chiral Primary Correlator
• Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
• Limiting Geometries of Two Circular Maldacena-Wilson Loop Operators

Cited by in corpus (39)

• Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• New supersymmetric Wilson loops in ABJ(M) theories
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• BPS Wilson loops in generic conformal N=2 SU(N) SYM theories
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Localization and AdS/CFT Correspondence
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Bremsstrahlung function, leading Luscher correction at weak coupling and localization
• Toward precision holography with supersymmetric Wilson loops
• S-duality, 't Hooft operators and the operator product expansion
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories
• Supersymmetric Wilson loops in N=4 SYM and pure spinors
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators
• Dressed Wilson Loops on S^2
• Ladder Limit for Correlators of Wilson Loops
• Impure Aspects of Supersymmetric Wilson Loops
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Emitted Radiation and Geometry
• Antisymmetric Wilson loops in $\mathcal{N}=4$ SYM beyond the planar limit
• Circular Wilson loops in defect $\mathcal{N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion
• Quantum 't Hooft loops of SYM N=4 as instantons of YM_2 in dual groups SU(N) and SU(N)/Z_N
• Supersymmetric Wilson loops in two dimensions and duality
• On a discrete symmetry of the Bremsstrahlung function in N=4 SYM
• Correlators of Hopf Wilson loops in the AdS/CFT correspondence
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• More on 't Hooft loops in N=4 SYM
• Equivariant and supersymmetric localization in QFT