Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-04-26
J.Stat.Mech.0710:P10003,2007
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, 2 tables, no figures; v2: references added, conjecture on exact four-loop twist-two result stated
Scientific paper
10.1088/1742-5468/2007/10/P10003
We prove that the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects. This is done by comparing the Bethe ansatz predictions for the four-loop anomalous dimension of finite-spin twist-two operators to BFKL constraints from high-energy scattering amplitudes in N=4 gauge theory. We find disagreement, which means that the ansatz breaks down for length-two operators at four-loop order. Our method supplies precision tools for multiple all-loop tests of the veracity of any yet-to-be constructed set of exact spectral equations. Finally we present a conjecture for the exact four-loop anomalous dimension of the family of twist-two operators, which includes the Konishi field.
Kotikov Anatoly V.
Lipatov Lev N.
Rej Adam
Staudacher Matthias
Velizhanin V. N.
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