A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5

TL;DR

This paper develops a semiclassical approach to analyze quantum fluctuation eigenvalues and compute the one-loop energy correction for a folded spinning superstring in AdS_5 x S^5, using two methods and deriving a small spin expansion.

Contribution

It introduces two methods for semiclassical eigenvalue analysis and provides an accurate calculation of one-loop energy corrections for the superstring.

Findings

Eigenvalues computed with high accuracy for certain string configurations.

Derived small spin Regge expansion using zeta function approximation.

Validated methods through comparison and analytical derivations.

Abstract

We systematically construct a semiclassical expansion for the eigenvalues of the 2nd order quantum fluctuations of the folded spinning superstring rotating in the AdS_3 part of AdS_5 x S^5 with two alternative methods; by using the exact expression of the Bloch momentum generated by the curvature induced periodic potentials and by using the large energy expansion of the dispersion relation. We then calculate the one-loop correction to the energy by summing over the eigenvalues. Our results are extremely accurate for strings whose ends are not too close to the AdS radius. Finally we derive the small spin Regge expansion in the context of zeta function approximation.