Five-loop Konishi from the Mirror TBA

TL;DR

The paper tests the consistency of the AdS/CFT TBA by computing the five-loop Konishi anomalous dimension using the $AdS_5\times S^5$ mirror TBA and comparing it to the generalized Lüscher result. By linearizing the simplified TBA around the asymptotic solution, it identifies that leading corrections arise from the auxiliary $Y_{M|vw}$ functions, with $\mathscr{Y}_{1|vw}$ driving the ABA correction and $Y_Q^{o}$-related terms entering at higher order. The authors numerically solve the resulting linear system to obtain $\mathscr{Y}_{1|vw}$ and show that the induced shift in the exact Bethe equations matches $\Phi^{(8)}$ from Lüscher, confirming five-loop agreement. This provides a strong cross-check of the TBA framework for the ${\rm AdS}_5\times {\rm S}^5$ system and motivates further analytic proofs of the observed equivalence.

Abstract

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.

Figures (1)

• Figure 1: In the upper picture the profiles of the functions ${\mathscr Y}_{1|vw}/g^8$ (blue) and ${\mathscr Y}_{2|vw}/g^8$ (purple) are depicted. They are obtained by solving numerically eq.(2.13). The lower picture contains the profiles of ${\mathscr Y}_{M|vw}/g^8$ for $M=2,3,4,5$. The absolute value of ${\mathscr Y}_{M|vw}$ decreases as $M$ increases.