6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values

TL;DR

This paper calculates the six-loop anomalous dimension of a specific operator in a deformed AdS/CFT setting, revealing the role of multiple zeta values and suggesting similar results for the Konishi operator.

Contribution

It provides a six-loop calculation of the anomalous dimension using AdS/CFT and evaluates Lüscher corrections at NNLO with multiple zeta values, advancing understanding of quantum corrections in deformed theories.

Findings

Six-loop anomalous dimension determined for a single impurity operator.

Lüscher correction evaluated at NNLO involving multiple zeta values.

Results suggest similar corrections for the Konishi operator at six loops.

Abstract

Anomalous dimension of the simplest nontrivial single impurity operator in the beta=1/2 deformed theory is determined at six loops from the AdS/CFT correspondence. L\"uscher correction is evaluated at next-to-next-to-leading order (NNLO) in terms of multiple zeta values. The result can be simplified into the products of simple zeta functions and the same form of the correction is expected for the Konishi operator at six loops, too.