Exact expressions for quantum corrections to spinning strings

TL;DR

This paper rigorously derives the quantum corrections to spinning string energies in AdS_5 x S^5, revealing analytic, non-analytic, and exponential terms, and clarifying their origins beyond the quantum Bethe ansatz approximation.

Contribution

It provides explicit expressions for quantum corrections to spinning strings, distinguishing between analytic and non-analytic contributions and their sources within the string fluctuations.

Findings

Analytic terms originate from S^3 fluctuations.

Non-analytic and exponential terms come from all directions in AdS_5 x S^5.

The quantum Bethe ansatz captures only the analytic terms.

Abstract

The one-loop worldsheet quantum corrections to the energy of spinning strings on R x S^3 within AdS_5 x S^5 are reexamined. The explicit expansion in the effective 't Hooft coupling \lambda'= \lambda/J^2 is rigorously derived. The expansion contains both analytic and non-analytic terms in \lambda', as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in \lambda'. It is shown that the analytic terms arise from string fluctuations within the S^3, whereas the non-analytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS_5 x S^5. We also comment on the case of spinning string in AdS_3 x S^1.