Circular semiclassical string solutions on AdS5× S5

Abstract

We discuss two semiclassical string solutions on AdS 5× 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 2 n and that its anomalous dimension scales as λ 1/4 mn , for large n. Next we consider a multiwrapped circular string pulsating on 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 2 n(1+ f( m 2 λ/(2 n) 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.