Reciprocity of gauge operators in N=4 SYM

TL;DR

This paper proves the generalized Gribov-Lipatov reciprocity for a class of operators in N=4 SYM at four-loop order, providing explicit anomalous dimensions and discussing potential wrapping corrections.

Contribution

It offers a complete proof of reciprocity for specific operators in N=4 SYM and derives a closed-form expression for their anomalous dimensions at four loops.

Findings

Reciprocity holds at four-loop order for the considered operators.

Derived a closed expression for the spin-dependent anomalous dimension.

Discussed implications of wrapping corrections on reciprocity.

Abstract

A recently discovered generalized Gribov-Lipatov reciprocity holds for the anomalous dimensions of various twist operators in N=4 SYM. Here, we consider a class of scaling psu(2,2|4) operators that reduce at one-loop to twist-3 maximal helicity gluonic operators. We extract from the asymptotic long-range Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections.