Sum rules for higher twist sl(2)operators in N=4 SYM

Details Sum rules for higher twist sl(2)operators in N=4 SYM Sum rules for higher twist sl(2)operators in N=4 SYM

2008-04-23

arxiv.org/abs/0804.3711v1

JHEP0806:103,2008

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, 2 eps figures

Scientific paper

10.1088/1126-6708/2008/06/103

The spectrum of anomalous dimensions of twist sl(2) operators in N=4 SYM has an intriguing feature in low twist 2 or 3. The anomalous dimension of the lowest state, dual a folded string on AdS_5 X S^5, can be computed by Bethe Ansatz at 3, 4 loops respectively as a simple closed function of the Lorentz spin. This feature is apparently lost at higher twist. We propose sum rules for the excited anomalous dimensions where closed expressions can still be provided, even at higher twist. We present several explicit three loop examples. Many structural regularities can be observed leading to closed expressions which depend parametrically both on the spin and the twist. They allow to compute the subleading term in the logarithmic large spin expansion of the sum rules as a compact simple function of the twist, in analogy with the recent results by Freyhult, Rej and Staudacher in arXiv:0712.2743 [hep-th].

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