Wilson loops in large N field theories

TL;DR

This paper introduces a method for computing Wilson loop expectation values in large N field theories using string and M-theory backgrounds, providing insights into quark-antiquark interactions across various dimensions.

Contribution

It presents a unified approach to calculate Wilson loop expectation values via string and M-theory worldsheet areas in diverse supergravity backgrounds.

Findings

Calculated quark-antiquark potential energies in different super-Yang-Mills theories.

Extended the method to non-conformal 2+1 dimensional theories.

Connected Wilson loop calculations to string and M-theory geometries.

Abstract

We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large N limit of field theories. We consider N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. We also consider the case of coincident M-theory fivebranes where one is lead to calculating the area of M-theory two-branes. We briefly discuss the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is non-conformal. In all these cases we calculate the energy of quark-antiquark pair.