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

References in corpus (5)

• Spinning strings and AdS/CFT duality
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Special contact Wilson loops

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• Wilson Loops in N=4 SYM and Fermion Droplets
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• Holography of Wilson-Loop Expectation Values with Local Operator Insertions
• The Bethe Ansatz Equations for Reflecting Magnons
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• Bethe ansatz equations for open spin chains from giant gravitons
• Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications