Boxing with Konishi

TL;DR

This paper discusses a scheme to compute the anomalous dimension of the Konishi operator in N=4 super Yang-Mills theory, addressing the wrapping problem in the spin chain approach at high loop orders.

Contribution

It proposes an operational method for calculating the Konishi operator's anomalous dimension at high loops, relating complex integrals to master graphs and avoiding infrared issues.

Findings

Most integrals relate to five master graphs solvable by partial integration

Remaining supergraph likely vanishing or finite, suitable for numerical analysis

Small numerator terms persist even at higher loop sectors

Abstract

The spin chain formulation of the operator spectrum of the N=4 super Yang-Mills theory is haunted by the problem of ``wrapping'', i.e. the inapplicability of the formalism for short spin chain length at high loop-order. The first instance of wrapping concerns the fourth anomalous dimension of the Konishi operator. While we do not obtain this number yet, we lay out an operational scheme for its calculation. The approach passes through a five- and six-loop sector. We show that all but one of the Feynman integrals from this sector are related to five master graphs which ought to be calculable by the method of partial integration. The remaining supergraph is argued to be vanishing or finite; a numerical treatment should be possible. The number of numerator terms remains small even if a further four-loop sector is included. There is no need for infrared rearrangements.