S-duality and Strong Coupling Behavior of Large N Gauge Theories with N=4 Supersymmetry

Abstract

We analyze the strong coupling behavior of the large N gauge theories in 4-dimensions with N=4 supersymmetry by making use of S-duality. We show that at large values of the coupling constant $\lambda =g_{YM}^{2}N$ the j-th non-planar amplitude $f_j(\lambda )(j=0,1,\mathrm{2...})$ behaves as $f_j(\lambda )\approx {\lambda }^j$. Implication of this behavior is discussed in connection with the supergravity theory on $Ad{S}_5\times S^5$ suggested by the CFT/AdS correspondence. S-duality of the gauge theory corresponds to the duality between the closed and open string loop expansions in the gravity/string theory.