Semiclassical quantization of rotating superstring in AdS_5 x S^5

TL;DR

This paper develops a semiclassical quantization method for superstrings in AdS_5 x S^5, deriving quantum corrections to classical rotating string solutions and supporting the link to gauge theory anomalous dimensions.

Contribution

It provides a detailed semiclassical quantization framework for rotating superstrings in AdS_5 x S^5, including 1-loop corrections and their implications for gauge/string duality.

Findings

1-loop correction to energy does not cancel for non-zero S.

Large S correction scales as ln S, matching classical behavior.

Supports the interpolation of classical E-S scaling to weak coupling in gauge theory.

Abstract

Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a classical solution describing string rotating in $AdS_5$ and boosted along large circle of $S^5$. The energy of the classical solution $E$ is a function of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the limiting cases S=0 and J=0 considered previously. We derive the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and compute the string 1-loop (large $\lambda= {R^4\over \a'^2}$) correction to the classical energy spectrum in the $(S,J)$ sector. We find that the 1-loop correction to the ground-state energy does not cancel for non-zero $S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no higher powers of $\ln S$ appearing. This supports the conjecture made in hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated to weak coupling to reproduce the corresponding operator anomalous dimension behaviour in gauge theory.