Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability

Abstract: We compute the contribution to the anomalous dimension of the twist-2 operators in N=4 SYM theory, which is proportional to the number of fermion loops inside Feynman diagrams or, formally, to the number of fermions. The result was obtained by the method based on the calculation of critical indices at the critical point by analogy with previous similar computations in scalar theories and in QCD. The obtained result is much simpler with compare to analogous results in QCD and almost satisfies the maximal transcedentality principle. A possible relation between the obtained result and integrability is discussed.