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

TL;DR

This paper derives sum rules for higher twist sl(2) operators in N=4 SYM, providing explicit expressions for anomalous dimensions at three loops and revealing structural regularities that facilitate computations at large spin.

Contribution

It introduces novel sum rules for excited anomalous dimensions of higher twist operators, extending the understanding beyond low twist cases in N=4 SYM.

Findings

Explicit three-loop sum rules for higher twist anomalous dimensions

Structural regularities enabling closed-form expressions

Compact formulas for large spin asymptotics depending on twist

Abstract

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].