Integrable Wilson loops

Abstract

The generalized quark-antiquark potential of N=4 supersymmetric Yang-Mills theory on S^3 x R calculates the potential between a pair of heavy charged particles separated by an arbitrary angle on S^3 and also an angle in flavor space. It can be calculated by a Wilson loop following a prescribed path and couplings, or after a conformal transformation, by a cusped Wilson loop in flat space, hence also generalizing the usual concept of the cusp anomalous dimension. In AdS_5 x S^5 this is calculated by an infinite open string. I present here an open spin-chain model which calculates the spectrum of excitations of such open strings. In the dual gauge theory these are cusped Wilson loops with extra operator insertions at the cusp. The boundaries of the spin-chain introduce a non-trivial reflection phase and break the bulk symmetry down to a single copy of psu(2|2). The dependence on the two angles is captured by the two embeddings of this algebra into \psu(2|2)^2, i.e., by a global rotation. The exact answer to this problem is conjectured to be given by solutions to a set of twisted boundary thermodynamic Bethe ansatz integral equations. In particular the generalized quark-antiquark potential or cusp anomalous dimension is recovered by calculating the ground state energy of the minimal length spin-chain, with no sites. It gets contributions only from virtual particles reflecting off the boundaries. I reproduce from this calculation some known weak coupling perturtbative results.

40 pages, 11 figures; v2-some formulas corrected, results unchanged

References in corpus (22)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gluon scattering amplitudes at strong coupling
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• On String S-matrix, Bound States and TBA
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• An Operator Product Expansion for Polygonal null Wilson Loops
• Supersymmetric Wilson loops on S^3
• Small deformations of supersymmetric Wilson loops and open spin-chains
• The cusp anomalous dimension at three loops and beyond
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Classical Open String Integrability
• Quark-antiquark potential in AdS at one loop
• The spectral problem for strings on twisted AdS_5 x S^5
• Twisting the Mirror TBA
• Twisted Bethe equations from a twisted S-matrix
• Cusped SYM Wilson loop at two loops and beyond
• Reflecting Magnon Bound States
• The Bethe Ansatz Equations for Reflecting Magnons
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT

Cited by in corpus (92)

• Exact results for the entanglement entropy and the energy radiated by a quark
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Hexagonalization of Correlation Functions
• Bootstrapping the half-BPS line defect
• The three-loop cusp anomalous dimension in QCD
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• The Quantum Spectral Curve of the ABJM theory
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Exact Slope and Interpolating Functions in ABJM Theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Structure constants at wrapping order
• Exact results for Wilson loops in arbitrary representations
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Roadmap on Wilson loops in 3d Chern-Simons-matter theories
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Quark--anti-quark potential in N=4 SYM
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• Exact Bremsstrahlung and Effective Couplings
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Introduction to the thermodynamic Bethe ansatz
• Towards the exact Bremsstrahlung function of ABJM theory
• Localization and AdS/CFT Correspondence
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Broken global symmetries and defect conformal manifolds
• The hexagon in the mirror: the three-point function in the SoV representation
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Resurgence of the Cusp Anomalous Dimension
• Fixing the Quantum Three-Point Function
• Bremsstrahlung function, leading Luscher correction at weak coupling and localization
• Exact Bremsstrahlung functions in ABJM theory
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
• Webs and Posets
• Subleading Regge limit from a soft anomalous dimension
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• On the Exact Interpolating Function in ABJ Theory
• The spectrum of tachyons in AdS/CFT
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
• Spin chain integrability in non-supersymmetric Wilson loops
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• A review of the AdS/CFT Quantum Spectral Curve
• Integrability of Smooth Wilson Loops in N=4 Superspace
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• The full angle-dependence of the four-loop cusp anomalous dimension in QED
• Quantum String Test of Nonconformal Holography
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Algebraic Curve for a Cusped Wilson Line
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Structure constants of operators on the Wilson loop from integrability
• Localization and Duality for ABJM Latitude Wilson Loops
• Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
• ABJM quantum spectral curve and Mellin transform
• Deformations of the circular Wilson loop and spectral (in)dependence
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Open Spin Chains from Determinant Like Operators in ABJM Theory
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• ABJM $\theta$-Bremsstrahlung at four loops and beyond: non-planar corrections
• Spectral curve for open strings attached to the Y=0 brane
• Emitted Radiation and Geometry
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Cusped Wilson lines in symmetric representations
• Two-Loop Integrability of ABJM Open Spin Chain from Giant Graviton
• Ironing out the crease
• An exact limit of ABJM
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• On analytical perturbative solution of ABJM quantum spectral curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• Boundary Perimeter Bethe Ansatz
• Spectral curve for gamma-deformed AdS/CFT
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• Wilson Loops and Integrability
• Boundary bound states and integrable Wilson loops in ABJM