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Wrapping corrections beyond the 𝔰𝔩(2) sector in 𝒩 = 4 SYM
Author(s) -
Beccaria M.,
Macorini G.,
Ratti C.
Publication year - 2012
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201200009
Subject(s) - bethe ansatz , spins , physics , spin (aerodynamics) , reciprocity (cultural anthropology) , twist , mathematical physics , operator (biology) , gluon , dimension (graph theory) , ansatz , coupling (piping) , particle physics , quantum chromodynamics , pure mathematics , mathematics , integrable system , repressor , chemistry , engineering , condensed matter physics , psychology , social psychology , biochemistry , geometry , transcription factor , thermodynamics , mechanical engineering , gene
The (2) sector of = 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 (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 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.