Quantum corrections to spinning strings in AdS5 x S5 and Bethe ansatz. A comparative study

We analyze quantum corrections to rigid spinning strings in AdS5 x S5. The one-loop worldsheet quantum correction to the string energy is compared to the finite-size correction from the quantum string Bethe ansatz. Expanding the summands of the string theory energy shift in the parameter 1/J2 = λ/J2 and subsequently resumming them yields a divergent result. However, upon zeta-function regularization this result agrees with the Bethe ansatz at the first three orders. We also perform an analogous computation in the limit of large winding number, which results in a disagreement with the string Bethe ansatz prediction. A similar mismatch is observed numerically. We comment on the possible origin of this discrepancy. (orig.)