Five loop Konishi from AdS/CFT

TL;DR

This paper computes the five-loop anomalous dimension of the Konishi operator in N=4 SYM using integrability techniques, revealing new features and consistency checks that advance understanding of AdS/CFT correspondence.

Contribution

It derives the five-loop Konishi anomalous dimension from the integrable string sigma model, including novel modifications to Bethe Ansatz and dressing phase effects.

Findings

Five-loop Konishi anomalous dimension computed from integrability.

Identification of modifications to Bethe Ansatz quantization.

Consistency with nontrivial transcendentality and pole cancellation.

Abstract

We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2 single impurity state in the beta deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features - a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions - simple transcendentality structure and cancellation of mu-term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.