On the fermionic frequencies of circular strings

Abstract

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