gauge theory and string theory is: ł’ &=&\
g\_2 &=& (4g\_s)(p\^+ ’)\^2\
g\^2\_[YM]{} &=& 4g\_s

Despite the correspondence of notation the string states listed in (\[st\],\[sts\]) are not the direct maps of the individual operators in (\[op\],\[ops\]). The reason is that the operators mix through nonplanar graphs [@bianchi; @pots2; @mit2] even in the free field theory whereas the eigenstates of the free string Hamiltonian in (\[sts\]) containing different numbers of strings are orthogonal. An operator $S$ effecting a change of basis in the gauge theory has been identified [@ucsb; @vv] which makes the gauge theory states in (\[ops\]) orthogonal in the free theory and it is the states obtained by applying $S^{-1}$ to those of (\[ops\]) which map into the string states of (\[sts\]).

Quantitative tests of the correspondence are based on the assumption that the light-cone Hamiltonian $P^- =H$ of string theory corresponds to the field theory operator $\D -J$, the difference between dilation and $R$-charge, through the relation \[dil\] - J = H In planar order the eigenstates of $\D-J$ are the individual states listed in (\[ops\]), and the order $g_2^0$ eigenvalues are \[eig\] ø(n,J\_0,J\_1,..J\_k) = 2 + ł’ with $s_0= J_0/J$. Operator mixing appears in order $g_2$, 