Massless L\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz

TL;DR

This paper investigates the limitations of the Bethe ansatz in AdS3 integrability, showing that massless Luscher F-terms account for discrepancies with semiclassical string results, unlike in AdS5 where it is more accurate.

Contribution

It demonstrates how massless Luscher F-terms explain the failure of the Bethe ansatz in AdS3, providing a new understanding of spectral corrections in this setting.

Findings

Massless Luscher F-terms account for discrepancies in AdS3 spectra.

Bethe ansatz inaccuracies in AdS3 are explained by these massless corrections.

The sum of all massless Luscher F-terms reproduces the observed differences.

Abstract

In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in AdS3, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez & Lopez, in which the su(2) sector Bethe equations (including one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations did not agree in AdS3xS3xT4, and we show that the sum of all massless Luscher F-terms can reproduce the difference.