The AdS5×S5AdS5×S5 superstring quantum spectrum from the algebraic curve

We propose a method for computing the energy level spacing around classical string solutions in AdS5×S5AdS5×S5. This method is based on the integrable structure of the string and can be applied to an arbitrary classical configuration. Our approach treats in equal footing the bosonic and fermionic excitations and provides an unambiguous prescription for the labeling of the fluctuation frequencies. Finally we revisit the computation of these frequencies for the SU(2)SU(2) and SL(2)SL(2) circular strings and compare our results to the existing ones.