Notes on supersymmetric Wilson loops on a two-sphere

Abstract

We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops in N=4 super Yang-Mills theory and their string theory duals. The operators are defined for arbitrary contours on a two-sphere in space-time, and they were conjectured to be captured perturbatively by 2d bosonic Yang-Mills theory. In the AdS dual, they are described by pseudo-holomorphic string surfaces living on a certain submanifold of AdS_5 x S^5. We show that the regularized area of these string surfaces is invariant under area preserving diffeomorphisms of the boundary loop, in agreement with the conjecture. Further, we find a connection between the pseudo-holomorphicity equations and an auxiliary sigma-model on S^3, which may help to construct new 1/8-BPS string solutions. We also show that the conjectured relation to 2d Yang-Mills implies that a connected correlator of two Wilson loops is computed by a Hermitian Gaussian two-matrix model. On the AdS dual side, we argue that the connected correlator is described by two disconnected disks interacting through the exchange of supergravity modes, and we show that this agrees with the strong coupling planar limit of the two-matrix model.

52 pages, Minor typos fixed and some comments added in Sec. 8

References in corpus (18)

• Holographic Wilson Loops
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Supersymmetric Wilson loops on S^3
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Dyonic Giant Magnons
• Generating AdS String Solutions
• A Generalized Scaling Function for AdS/CFT
• Pohlmeyer reduction revisited
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• On reduced models for superstrings on AdS_n x S^n
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Dynamics of Flux Tubes in Large N Gauge Theories
• Operator product expansion of higher rank Wilson loops from D-branes and matrix models
• Calibrated Surfaces and Supersymmetric Wilson Loops
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• Large Winding Sector of AdS/CFT
• A prediction for bubbling geometries

Cited by in corpus (39)

• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• 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
• Analytic Solution of Bremsstrahlung TBA
• New supersymmetric Wilson loops in ABJ(M) theories
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• 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
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Toward precision holography with supersymmetric Wilson loops
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• 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
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Spectral form factor and semi-circle law in the time direction
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Differential identities for the structure function of some random matrix ensembles
• A matrix model for the latitude Wilson loop in ABJM theory
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators
• Unitary Chern-Simons matrix model and the Villain lattice action
• Dressed Wilson Loops on S^2
• Dyson equations for correlators of Wilson loops
• Torus knot polynomials and susy Wilson loops
• Impure Aspects of Supersymmetric Wilson Loops
• Ladder Limit for Correlators of Wilson Loops
• Circular Wilson loops in defect $\mathcal{N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion
• Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories
• Correlators of Hopf Wilson loops in the AdS/CFT correspondence
• Ladder exponentiation for generic large symmetric representation Wilson loops
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• Weak Coupling Expansion of Yang-Mills Theory on Recursive Infinite Genus Surfaces
• Loop equations for generalised eigenvalue models