Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5

TL;DR

This paper calculates one-loop quantum corrections to the dispersion relations of excitations in a long spinning superstring in AdS_5 x S^5, providing insights into quantum string dynamics and their agreement with integrability-based methods.

Contribution

It presents the first perturbative computation of one-loop dispersion relations for string excitations in AdS_5 x S^5, including the stability analysis of the heaviest mode.

Findings

One-loop corrections to dispersion relations are computed.

The heaviest AdS mode is found to be stable at one-loop.

Results partially agree with the asymptotic Bethe ansatz computations.

Abstract

We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the leading one-loop corrections to the dispersion relations of the excitations near a long spinning string in AdS. This investigation is partially motivated by the OPE-based approach to the computation of the expectation value of null polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial agreement with the recent asymptotic Bethe ansatz computation in arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in the ABA approach) is stable and has a corrected one-loop dispersion relation similar to the other massive modes. Its stability might hold also at the next-to-leading order as we suggest using a unitarity-based argument.