Small deformations of supersymmetric Wilson loops and open spin-chains

Abstract

We study insertions of composite operators into Wilson loops in N=4 supersymmetric Yang-Mills theory in four dimensions. The loops follow a circular or straight path and the composite insertions transform in the adjoint representation of the gauge group. This provides a gauge invariant way to define the correlator of non-singlet operators. Since the basic loop preserves an SL(2,R) subgroup of the conformal group, we can assign a conformal dimension to those insertions and calculate the corrections to the classical dimension in perturbation theory. The calculation turns out to be very similar to that of single-trace local operators and may also be expressed in terms of a spin-chain. In this case the spin-chain is open and at one-loop order has Neumann boundary conditions on the type of scalar insertions that we consider. This system is integrable and we write the Bethe ansatz describing it. We compare the spectrum in the limit of large angular momentum both in the dilute gas approximation and the thermodynamic limit to the relevant string solution in the BMN limit and in the full AdS_5 x S^5 metric and find agreement.

40 pages, amstex, 4 figures. V2: Corrected eqn (2.14) and some equations in section 5. Version to appear in JHEP

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• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Generalized quark-antiquark potential at weak and strong coupling
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• Wilson Loops in N=4 SYM and Fermion Droplets
• Analytic Solution of Bremsstrahlung TBA
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
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• 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
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• 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
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• On the D3-brane description of some 1/4 BPS Wilson loops
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• A Semiclassical String Description of Wilson Loop with Local Operators
• Broken global symmetries and defect conformal manifolds
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Holography of Two-point Functions in the Spinning String/Spin Chain Correspondence
• Holography of Wilson-Loop Expectation Values with Local Operator Insertions
• Reflecting magnons from D7 and D5 branes
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• On boundary correlators in Liouville theory on AdS${}_2$
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• The spectrum of tachyons in AdS/CFT
• Space-like minimal surfaces in AdS x S
• The Bethe Ansatz Equations for Reflecting Magnons
• Spin chain integrability in non-supersymmetric Wilson loops
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Exact momentum fluctuations of an accelerated quark in N=4 super Yang-Mills
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Non-relativistic String and D-branes on AdS_5 x S^5 from Semiclassical Approximation
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• Non-abelian Toda theory on AdS${}_2$ and AdS${}_2$/CFT${}_2^{1/2}$ duality
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Algebraic Curve for a Cusped Wilson Line
• Wilson-loop One-point Functions in ABJM Theory
• Structure constants of operators on the Wilson loop from integrability
• Double-helix Wilson loops: case of two angular momenta
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates
• Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary Conditions
• 1/3 BPS loops and defect CFTs in ABJM theory
• Deformations of the circular Wilson loop and spectral (in)dependence
• Fermionic Bogomolnyi-Prasad-Sommerfield Wilson loops in four-dimensional $\mathcal{N}=2$ superconformal gauge theories
• Open Spin Chains from Determinant Like Operators in ABJM Theory
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton
• Semi-classical correlator for 1/4 BPS Wilson loop and chiral primary operator with large R-charge
• Defect Localized Entropy: Renormalization Group and Holography
• D5-brane boundary reflection factors
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• On anomalous conformal Ward identities for Wilson loops on polygon-like contours with circular edges
• BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Quantum deformation of cubic string field theory
• A tunneling picture of dual giant Wilson loop
• Exact Results in Supersymmetric Gauge Theories
• More Fermionic Supersymmetric Wilson loops in Four Dimensions
• On some 1/4 BPS Wilson-'t Hooft loops
• Wilson loops as defects in N=2 conformal field theories
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• Holographic Wilson Loop One-point Functions in ABJM Theory
• Universal sectors in superconformal defects
• Boundary bound states and integrable Wilson loops in ABJM