Correlation function of circular Wilson loops at strong coupling

2013/09/23 by Amit Dekel, Thomas Klose
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Correlation function (quantum field theory) #Gauge theory #Geometry #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Partition function (quantum field theory) #Phase transition #Physics #Quadratic equation #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Regularization (linguistics) #Wilson loop #hep-th

paper · pdf · doi:10.1007/jhep11(2013)117

44 pages, 14 figures. v2: references added

arxiv created 2013/09/23 · openalex publication_date 2013/11/01 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the correlation function of two circular Wilson loops at strong coupling in N=4 super Yang-Mills theory. Using the AdS/CFT correspondence, the problem maps to finding the minimal surface between two circles defined on the boundary of AdS, and the fluctuations around the classical solution in AdS₅ x S⁵. At the classical level, we derive the string solution in H₃ x S¹ explicitly, and focus on properties such as stability and phase transition. Furthermore, a computation of the associated algebraic curve is given. At the quantum level, the one-loop partition function is constructed by introducing quadratic bosonic and fermionic fluctuations around the classical solution, embedded in AdS₅ x S⁵. We find an analytic, formal expression for the partition function in terms of an infinite product by employing the Gel'fand-Yaglom method and supersymmetric regularization. We regulate the expression and evaluate the partition function numerically.

Citations

• Phase transition in Wilson loop correlator from AdS/CFT correspondence
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• HEUN FUNCTIONS VERSUS ELLIPTIC FUNCTIONS
• One-loop effective action of the holographic antisymmetric Wilson loop
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• The large N limit of superconformal field theories and supergravity

Cited by

• On shape dependence of holographic entanglement entropy in AdS4/CFT3