The Bajnok-Janik formula and wrapping corrections

TL;DR

This paper demonstrates that wrapping corrections to Bethe equations in the AdS5 x S5 string sigma-model match the Bajnok-Janik formula up to order g^8, linking TBA and Lüscher approaches.

Contribution

It establishes the equivalence of wrapping corrected Bethe equations derived from TBA and generalized Lüscher formulas for minimal energy operators.

Findings

Wrapping corrected Bethe equations match Bajnok-Janik formula up to O(g^8).

Simplified TBA equations are derived for the AdS5 x S5 string sigma-model.

Applications extend to various relativistic integrable models.

Abstract

We write down the simplified TBA equations of the $AdS_5 \times S^5$ string sigma-model for minimal energy twist-two operators in the sl(2) sector of the model. By using the linearized version of these TBA equations it is shown that the wrapping corrected Bethe equations for these states are identical, up to O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach (Bajnok-Janik formula). Applications of the Bajnok-Janik formula to relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and the SU(n) principal sigma models, are also discussed.