Correlation Function of Circular Wilson Loops at Strong Coupling

TL;DR

This paper investigates the correlation of two circular Wilson loops at strong coupling in N=4 super Yang-Mills theory using AdS/CFT, deriving classical solutions, analyzing stability, phase transitions, and computing quantum fluctuations.

Contribution

It provides explicit classical string solutions, analyzes their stability and phase transitions, and computes the one-loop quantum corrections using algebraic curves and regularization methods.

Findings

Derived explicit classical string solutions in AdS_3 x S^1.

Analyzed stability and phase transition properties of the solutions.

Computed the one-loop partition function numerically with regularization.

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 AdS_5 x S^5. At the classical level, we derive the string solution in H_3 x S^1 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 AdS_5 x S^5. 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.