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

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 space and charge in S5. 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.