Wilson Loops in LargeNField Theories

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 $N=4\mathrm{}$ $(3+1)$-dimensional supersymmetric Yang-Mills theory. The prescription involves calculating the area of a fundamental string world sheet in certain supergravity backgrounds. We also consider the case of coincident $M$-theory five-branes where one is led to calculating the area of $M$-theory two-branes. We briefly discuss the computation for $(2+1)$-dimensional supersymmetric Yang-Mills theory with 16 supercharges which is nonconformal. In all of these cases, we calculate the energy of a quark-antiquark pair.