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

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.