On the Fermionic Frequencies of Circular Strings

TL;DR

This paper investigates discrepancies in fermionic frequency calculations for circular strings in AdS spaces, showing that careful treatment of transition matrices in the spin bundle resolves these differences.

Contribution

It clarifies the origin of discrepancies in semiclassical fluctuation spectra and introduces a method to reconcile different computational approaches.

Findings

Discrepancies in frequencies are due to transition matrix effects.

Proper accounting of spin bundle transitions removes the frequency shifts.

Results unify algebraic curve and worldsheet computations.

Abstract

We revisit the semiclassical computation of the fluctuation spectrum around different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from the Green-Schwarz action. It has been known that the results for these frequencies obtained from the algebraic curve and from the worldsheet computations sometimes do not agree. In particular, different methods give different results for the half-integer shifts in the mode numbers of the frequencies. We find that these discrepancies can be removed if one carefully takes into account the transition matrices in the spin bundle over the target space.