Wilson loops and Riemann theta functions II

Abstract

In this paper we extend and simplify previous results regarding the computation of Euclidean Wilson loops in the context of the AdS/CFT correspondence, or, equivalently, the problem of finding minimal area surfaces in hyperbolic space (Euclidean AdS3). If the Wilson loop is given by a boundary curve X(s) we define, using the integrable properties of the system, a family of curves X(lambda,s) depending on a complex parameter lambda known as the spectral parameter. This family has remarkable properties. As a function of lambda, X(lambda,s) has cuts and therefore is appropriately defined on a hyperelliptic Riemann surface, namely it determines the spectral curve of the problem. Moreover, X(lambda,s) has an essential singularity at the origin lambda=0. The coefficients of the expansion of X(lambda,s) around lambda=0, when appropriately integrated along the curve give the area of the corresponding minimal area surface. Furthermore we show that the same construction allows the computation of certain surfaces with one or more boundaries corresponding to Wilson loop correlators. We extend the area formula for that case and give some concrete examples. As the main example we consider a surface ending on two concentric circles and show how the boundary circles can be deformed by introducing extra cuts in the spectral curve.

LaTeX, 45 pages, 10 figures. v2: typos corrected, references added

References in corpus (10)

• Gluon scattering amplitudes at strong coupling
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• Form factors at strong coupling via a Y-system
• Supersymmetric Wilson loops on S^3
• Generating AdS String Solutions
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Cited by in corpus (15)

• Wilson loops and minimal area surfaces in hyperbolic space
• On shape dependence of holographic entanglement entropy in AdS4/CFT3
• Master Symmetry for Holographic Wilson Loops
• Minimal area surfaces dual to Wilson loops and the Mathieu equation
• Semiclassical $p$-branes in hyperbolic space
• Static Elliptic Minimal Surfaces in AdS(4)
• Dual conformal transformations of smooth holographic Wilson loops
• Minimal area surfaces in AdS${}_3$ through integrability
• From algebraic curve to minimal surface and back
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• Geometric Flow Description of Minimal Surfaces
• Dressed Minimal Surfaces in AdS${}_4$
• Wilson Loops and Integrability
• Holographic Calculations of Euclidean Wilson Loop Correlator in Euclidean anti-de Sitter Space
• Novel aspects of integrability for NLSMs in symmetric spaces