Abstract
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space. We use a formalism introduced recently by Kruczenski to perturbatively compute the area corresponding to boundary contours which are deformations of the circle. Our perturbative expansion is carried to high orders compared with the wavy approximation and yields new analytic results. The regularized area is invariant under a one parameter family of continuous deformations of the boundary contour which are not related to the global symmetry of the problem. We show that this symmetry of the Wilson loops breaks at weak coupling at an a priori unexpected order in the perturbative expansion. We also study the corresponding Lax operator and algebraic curve for these solutions.
Highlights
Integrability properties of Wilson loops, and in particular Euclidean Wilson loops
We study Euclidean Wilson loops at strong coupling using the AdS/CFT correspondence, where the problem is mapped to finding the area of minimal surfaces in Hyperbolic space
We show that this symmetry of the Wilson loops breaks at weak coupling at an a priori unexpected order in the perturbative expansion
Summary
We briefly repeat the analysis presented by Kruczenski in [11], where the reader is referred to for more details. Following [8] we rewrite the embedding coordinates in terms of a matrix X = Xμσμ where σμ = {1, σi} and σi are the Pauli matrices In this way the constraints and equations of motion are given by. In case where λ is a phase this still corresponds to a string solution, generally defined by a different contour, with the same area for the minimal surface ending on the original contour. This deformation of the original contour is not related to any obvious global symmetry of the problem and we shall call such deformations λ-deformations throughout the paper. In the following we shall approach the problem perturbatively around the simplest available solutions, namely the circle and the infinite line, and show that this formalism enables us to perform such a perturbative expansion very efficiently without finding the minimal surface explicitly, and to reach very high orders in the perturbation expansion compared to the wavy approximation
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