Supersymmetric Wilson loops on S^3

Abstract

This paper studies in great detail a family of supersymmetric Wilson loop operators in N=4 supersymmetric Yang-Mills theory we have recently found. For a generic curve on an S^3 in space-time the loops preserve two supercharges but we will also study special cases which preserve 4, 8 and 16 supercharges. For certain loops we find the string theory dual explicitly and for the general case we show that string solutions satisfy a first order differential equation. This equation expresses the fact that the strings are pseudo-holomorphic with respect to a novel almost complex structure we construct on AdS_4 x S^2. We then discuss loops restricted to S^2 and provide evidence that they can be calculated in terms of similar observables in purely bosonic YM in two dimensions on the sphere.

Latex, 84 pages, 4 figures. v2: minor changes, references added; to appear in JHEP

References in corpus (64)

• Gauge Theory Correlators from Non-Critical String Theory
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Wilson loops in large N field theories
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Gluon scattering amplitudes at strong coupling
• A semi-classical limit of the gauge/string correspondence
• A Strong Coupling Test of S-Duality
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Two Dimensional Gauge Theories Revisited
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• Bethe Ansatz for Quantum Strings
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Wilson Loops and Minimal Surfaces
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Multi-spin string solutions in AdS_5 x S^5
• Holography and Defect Conformal Field Theories
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Structure functions for large $x$ and renormalization of Wilson loops
• Holographic Wilson Loops
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Comments on operators with large spin
• All-genus calculation of Wilson loops using D-branes
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Supersymmetric Wilson loops
• On gravitational description of Wilson lines
• Wilson Loops as D3-Branes
• Higher rank Wilson loops from a matrix model
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Gravity duals of half-BPS Wilson loops
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Supersymmetry and generalized calibrations
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Intersecting D3-branes and Holography
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD
• On the Strong Coupling Scaling Dimension of High Spin Operators
• More supersymmetric Wilson loops
• Bubbling Geometries for Half BPS Wilson lines
• Wilson Loops in N=4 SYM and Fermion Droplets
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze
• Strong-coupling expansion of cusp anomaly from quantum superstring
• AdS Calibrations
• Light-Cone Wilson Loops and the String/Gauge Correspondence
• S-Duality and the Dyon Spectrum in N=2 Super Yang-Mills Theory
• Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription
• Instanton corrections to circular Wilson loops in N=4 Supersymmetric Yang-Mills
• Holographic Gauge Theories in Background Fields and Surface Operators
• On the D3-brane description of some 1/4 BPS Wilson loops
• Superisometries of the adS*S Superspace
• Operator product expansion of higher rank Wilson loops from D-branes and matrix models
• Calibrated Surfaces and Supersymmetric Wilson Loops
• Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription
• Properties of Chiral Wilson Loops
• On 1/2-BPS Wilson-'t Hooft loops
• A prediction for bubbling geometries

Cited by in corpus (116)

• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Gauge Theory Loop Operators and Liouville Theory
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Generalized quark-antiquark potential at weak and strong coupling
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• Integrable Wilson loops
• 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
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• 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
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• 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
• Notes on supersymmetric Wilson loops on a two-sphere
• 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
• Spectral curves, emergent geometry, and bubbling solutions for Wilson loops
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Precision calculation of 1/4-BPS Wilson loops in AdS${}_5\times S^5$
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Localization and AdS/CFT Correspondence
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions
• 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
• The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details
• Wilson Loops and Chiral Correlators on Squashed Sphere
• BPS Wilson Loops on S^2 at Higher Loops
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• 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
• Wilson loops and minimal area surfaces in hyperbolic space
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Wilson loops and Riemann theta functions II
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Monopoles and Wilson Lines
• Branes from Light: Embeddings and Energetics for Symmetric $k$-Quarks in $\mathcal{N}=4$ SYM
• Zeta-function Regularization of Holographic Wilson Loops
• Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Interpolating Wilson loops and enriched RG flows
• A matrix model for the latitude Wilson loop in ABJM theory
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators
• Double-helix Wilson loops: case of two angular momenta
• Wilson Loops and Chiral Correlators on Squashed Spheres
• On gauge/string correspondence and mirror symmetry
• Observations on BPS observables in 6d
• Wilson Loops in 3d QFT from D-branes in AdS(4) x CP**3
• Localization and Duality for ABJM Latitude Wilson Loops
• The topological line of ABJ(M) theory
• Dressed Wilson Loops on S^2
• Dyson equations for correlators of Wilson loops
• Torus knot polynomials and susy Wilson loops
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Impure Aspects of Supersymmetric Wilson Loops
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Minimal area surfaces dual to Wilson loops and the Mathieu equation
• BPS Wilson loops in Minkowski spacetime and Euclidean space
• Holographic Cusped Wilson loops in $q$-deformed $Ad{S}_5\times S^5$ Spacetime
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• Emitted Radiation and Geometry
• Classifying BPS bosonic Wilson loops in 3d $\mathcal{N}=4$ Chern-Simons-matter theories
• Cusped Wilson lines in symmetric representations
• M2-doughnuts
• Minimal area surfaces in AdS_{n+1} and Wilson loops
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Supersymmetric Wilson Loops in Diverse Dimensions
• Ironing out the crease
• Functional Determinants of Radial Operators in $Ad{S}_2$
• 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
• Dual conformal transformations of smooth holographic Wilson loops
• Quantum 't Hooft loops of SYM N=4 as instantons of YM_2 in dual groups SU(N) and SU(N)/Z_N
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited
• Supersymmetric Wilson loops in two dimensions and duality
• Wilson Loops from D-branes in AdS(4) X CP**3 with B-NS Holonomy
• Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
• Interpolating Bremsstrahlung function in ABJM
• BPS surface operators and calibrations
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• Correlators of Hopf Wilson loops in the AdS/CFT correspondence
• Ladder exponentiation for generic large symmetric representation Wilson loops
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• D-brane Description of New Open String Solutions in AdS(5)
• Global AdS Picture of 1/2 BPS Wilson Loops
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• More on 't Hooft loops in N=4 SYM
• BPS Wilson Loop T-dual to Spinning String in AdS5xS5
• Wilson loops for triangular contours with circular edges
• Loop equations for generalised eigenvalue models
• Generalized quark-antiquark potential in AdS/CFT
• More Fermionic Supersymmetric Wilson loops in Four Dimensions
• Holographic Wilson Loop One-point Functions in ABJM Theory
• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$
• On the D5-brane description of $\frac{1}{4}$-BPS Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory
• Lattice defect networks in 2d Yang-Mills