Superspace calculation of the four-loop spectrum in N = 6 supersymmetric Chern-Simons theories

Using N = 2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) × SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h (λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv: 0908.2463 and arXiv: 0912.3460. We also discuss possible scenarios for an all-loop function h (X) that interpolates between weak and strong couplings