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

Understand

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.