Circular Semiclassical String Solutions on AdS_5 x S_5

TL;DR

This paper analyzes two semiclassical string solutions in AdS_5 x S_5, calculating their energies and operator dimensions, and explores their implications within the AdS/CFT correspondence.

Contribution

It introduces new semiclassical string solutions with detailed energy and dimension calculations, extending understanding of string dynamics and gauge theory duals.

Findings

Energy scales as λ^{1/4}√(mn) for pulsating strings.

Operator dimensions depend on a series expansion in m^2λ/(2n)^2.

Results connect string solutions to gauge theory operator dimensions.

Abstract

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.