A Universality Test of the Quantum String Bethe Ansatz

TL;DR

This work tests the universality of the quantum corrected string Bethe ansatz (SBA) by showing that its non-analytic, one-loop corrections reproduce the string sigma-model results for rational three-spin strings with two equal spins. By deriving SBA-based non-analytic energy corrections in the ${rak{su}}(3)$ sector and matching them to an explicit string sigma-model calculation, the authors uniquely determine the coefficients $δc_{r,s}$ and confirm the conjectured universal form $δc_{r,s}= -8 (r-1)(s-1)/((r+s-2)(s-r))$ for odd $r+s$ (zero for even $r+s$). The analysis then yields predictions for general three-spin configurations and winding numbers, supporting the universality of the dressing phase across sectors. While the results reinforce the SBA as a valid framework for leading quantum corrections, they also underscore the need for a full quantum string quantization to resolve higher-loop discrepancies with gauge theory.

Abstract

We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin strings with two out of the three spins identical. Subsequently, we use the quantum corrected string Bethe ansatz to predict the exact form of the non-analytic terms for the generic rational three-spin string.