Circular Semiclassical String Solutions on AdS_5 x S_5

We discuss two semiclassical string solutions on $AdS_5\times S_5$. In the first case, we consider a multiwrapped circular string pulsating in the radial direction of $AdS_5$, but fixed to a point on the $S_5$. We compute the energy of this motion as a function of a large quantum number $n$. We identify the string level with $mn$, where $m$ is the number of string wrappings. Using the AdS/CFT correspondence, we argue that the bare dimension of the corresponding gauge invariant operator is $2n$ and that its anomalous dimension scales as $\lamba^{1/4}\sqrt{mn}$, for large $n$. Next we consider a multiwrapped circular string pulsating about two opposite poles of the $S_5$. We compute the energy of this motion as a function of a large quantum number, $n$ where again the string level is given as $mn$. We find that the dimension of the corresponding operator is $2n(1+f(m^2\la/(2n)^2))$, where $f(x)$ is computible as a series about $x=0$ and where it is analytic. We also compare this result to the BMN result for large $J$ operators. In both cases, we give conjectures for the gauge invariant operators dual to the string modes.