Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study

TL;DR

This paper compares quantum corrections to spinning strings in AdS(5)xS(5) from string theory and Bethe ansatz, finding agreement at low orders but discrepancies at large winding numbers, highlighting subtle issues in the correspondence.

Contribution

It provides a detailed comparison between one-loop string energy corrections and Bethe ansatz predictions, revealing where they agree and diverge.

Findings

Agreement with Bethe ansatz at first three orders after regularization.

Disagreement at large winding number limit.

Numerical mismatch observed in the large winding number regime.

Abstract

We analyze quantum corrections to rigid spinning strings in AdS(5)xS(5). 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 \lambda/J^2 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.