Quantum corrections to spinning strings inAdS5×S5and Bethe ansatz: a comparative study

We analyze quantum corrections to rigid spinning strings in AdS(5)xS(5). Theone-loop worldsheet quantum correction to the string energy is compared to thefinite-size correction from the quantum string Bethe ansatz. Expanding thesummands of the string theory energy shift in the parameter \lambda/J^2 andsubsequently resumming them yields a divergent result. However, uponzeta-function regularization this result agrees with the Bethe ansatz at thefirst three orders. We also perform an analogous computation in the limit oflarge winding number, which results in a disagreement with the string Betheansatz prediction. A similar mismatch is observed numerically. We comment onthe possible origin of this discrepancy.Comment: 33 pages, 9 figure