Wrapping corrections beyond the sl(2) sector in N=4 SYM

TL;DR

This paper computes the four-loop wrapping correction to anomalous dimensions of twist operators beyond the sl(2) sector in N=4 SYM, revealing new insights into their behavior at weak coupling and large spin.

Contribution

It introduces a novel calculation of wrapping corrections for non-sl(2) operators using the Y-system, extending understanding beyond the well-studied sector.

Findings

Derived a closed-form four-loop correction as a function of spin n.

Confirmed generalized Gribov-Lipatov reciprocity at large n.

Presented a BFKL-like equation for unphysical negative spin.

Abstract

The sl(2) sector of N=4 SYM theory has been much studied and the anomalous dimensions of those operators are well known. Nevertheless, many interesting operators are not included in this sector. We consider a class of twist operators beyond the sl(2) subsector introduced by Freyhult, Rej and Zieme. They are spin n, length-3 operators. At one-loop they can be identified with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS_5 space and charge in S^5. We exploit the Y-system to compute the leading weak-coupling four loop wrapping correction to their anomalous dimension. The result is written in closed form as a function of the spin n. We combine the wrapping correction with the known four loop asymptotic Bethe Ansatz contribution and analyze special limits in the spin n. In particular, at large n, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative unphysical spin, we present a simple BFKL-like equation predicting the rightmost leading poles.