Twist-three at five loops, Bethe Ansatz and wrapping

We present a formula for the five-loop anomalous dimension of N = 4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Lu ̈scher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous di- mension at four-loops wrapping effects are of order (log2 M/M2) for large values of the spin