Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM

TL;DR

This paper computes four-loop wrapping corrections for certain twist operators in N=4 SYM beyond the sl(2) sector, analyzing their properties at weak and strong coupling, and confirming reciprocity and BFKL-like behavior.

Contribution

It provides the first closed-form four-loop wrapping correction for non-sl(2) operators in N=4 SYM and explores their asymptotic and special limit behaviors.

Findings

Proves generalized Gribov-Lipatov reciprocity at large N.

Derives a BFKL-like equation for unphysical negative spin.

Provides a closed-form expression for four-loop wrapping correction.

Abstract

We consider N=4 SYM and a class of spin N, length-3, twist operators beyond the well studied sl(2) subsector. They can be identified at one-loop with three gluon operators. At strong coupling, they are associated with spinning strings with two spins in AdS5. 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.