Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM

We propose a closed expression for the three loop anomalous dimension of a class of twist-3 operators built with gauge fields and covariant derivatives. To this aim, we solve the long-range Bethe Ansatz equations at finite spin and provide a consistent analytical formula obtained assuming maximal transcendentality violation as suggested by the known one-loop anomalous dimension. The final result reproduces the universal cusp anomalous dimension and obeys recursion relations inspired by the principle of reciprocity invariance.