Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-09-05
Nucl.Phys. B648 (2003) 203-214
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, LaTeX;v3 minor error fixed;v4 reference added, sec 4 clarified and expanded slightly; v5 corrected a term in 4.12 an
Scientific paper
10.1016/S0550-3213(02)00966-5
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 \lambda^{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\lambda/(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.
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