Stringy effects for spinning strings and the Bethe ansatz

The one-loop worldsheet corrections to spinning strings in the sl(2) subsector of AdS5 × S5 are compared to the quantum string Bethe ansatz. The evaluation of the energy shift is performed in two regimes: a) in the large limit, using zeta-function regularization and b) in the limit of large winding number. The first computation agrees with the Bethe ansatz in the first three orders while the second computation leads to a disagreement with the string Bethe ansatz prediction at leading order. Careful analysis of the zeta-function regularization shows, that in this approach perturbative as well as non-perturbative terms in the string sums are missed. Hence, this together with the result b), implies that the proposed quantum string Bethe equations do not reproduce all terms in the exact string result