charge $J$. The correlation functions of these operators are governed by two parameters, the effective coupling $\l' = g^2_{YM}N/J^2$ and genus expansion parameter $g_2 =J^2/N$, and one works in the limit $N \to \infty,~~J \to \infty$ with $J^2/N$ fixed.

One family of operators commonly considered are single- and multi-trace operators with two scalar “impurity” fields $\f (x), \j (x)$ and $J$ “substrate” fields $Z(x)$, \[op\] \_n\^[J\_0]{}=\_[l=0]{}\^[J\_0]{}e\^ (Z\^lZ\^[J\_0-l]{}). and \[ops\] \_n\^[J\_0,J\_1,…J\_k]{}=:O\_n\^[J\_0]{}O\^[J\_1]{}…O\^[J\_k]{}:, with $J = J_0+J_2+\cdots J_k.$ Here $O^{J}$ is the chiral primary operator, \^J=(Z\^J).

The states of superconformal $\cn =4$ gauge theory on $R \times S^3$ which correspond to these operators[^3] are dual to states of the Type IIB superstring quantized in light-cone gauge in the background pp-wave metric and 5-form: ds\^2 &=& -4dx\^+dx\^- - \^2 x\^ix\^idx\^[+2]{}+dx\^idx\^i; i=1,…, 8,\
F\_[+1234]{} &=& F\_[+5678]{} = . The dual string states are those obtained from the ground state $|p^+ \ra$ with light-cone momentum $p^+$ by the action of creation operators $a^*_\f (n),~a^*_\j (n)$ with world-sheet momentum $n$. More specifically one considers single- and multi-string states: \[st\] a\^\*\_(n) a\^\*\_(-n)|p\^+ and \[sts\] a\^\*\_(n) a\^\*\_(-n)|p\_0\^+|p\_1\^+|p\_k\^+ where light-cone momenta $p_i^+$ of individual string states are related to corresponding $R$-charges by $\m p_i^+\a'=\frac{J_i}{\sqrt{g^2_{YM}N}}$. The relation between the parameters of 