Six-loop Konishi anomalous dimension from the Y-system

TL;DR

This work uses a finite closed set of functional equations for the AdS/CFT Y-system to compute the Konishi operator’s anomalous dimension up to six loops. By reformulating the GKLV equations and implementing a perturbative expansion around the asymptotic solution, the authors derive the wrapping corrections and the exact Bethe equations, accounting for Bethe-root displacement and finite-volume effects. The six-loop energy, expressed in terms of Euler–Zagier sums or zeta values, matches independent Lüscher calculations and numerical estimates, providing a strong cross-check of the finite-Y-system approach and paving the way toward higher-order (double-wrapping) analyses. The methodology demonstrates a concrete, systematic procedure to extract wrapping corrections from a finite functional framework, with potential applications to other states and higher-loop orders.

Abstract

We compute the Konishi anomalous dimension perturbatively up to six loop using the finite set of functional equations derived recently by Gromov, Kazakov, Leurent and Volin. The recursive procedure can be in principle extended to higher loops, the only obstacle being the complexity of the computation.

Figures (1)

• Figure 1: Structure of the perturbative computation.