A universality test of the quantum string Bethe ansatz

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.