Wilson Loops in Large<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">N</mml:mi></mml:math>Field 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 $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$ $(3+1)$-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.