On the Fermionic Frequencies of Circular Strings

Understand

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.