5-loop Konishi from linearized TBA and the XXX magnet

TL;DR

The paper addresses the 5-loop wrapping correction to the Konishi anomalous dimension in N=4 SYM within the AdS/CFT integrability framework. It develops a linearized TBA formalism around the asymptotic solution and relates the resulting bilinear problem for vw-strings to the inhomogeneous XXX spin-1/2 chain, enabling analytic computation via the XXX TBA. The authors prove analytically that the 5-loop TBA result matches the generalized Lüscher formula result of BJ09, strengthening the consistency between TBA and Lüscher approaches for wrapping corrections. This work clarifies the structural link between AdS/CFT finite-size effects and XXX magnet integrability, providing a robust cross-check of higher-loop wrapping corrections.

Abstract

Using the linearized TBA equations recently obtained in [arXiv:1002.1711] we show analytically that the 5-loop anomalous dimension of the Konishi operator agrees with the result obtained previously from the generalized Luscher formulae. The proof is based on the relation between this linear system and the XXX model TBA equations.