  In arXiv:0908.2463 we computed the four-loop correction to a function
depending on the 't Hooft coupling(s) that appears in the magnon dispersion
relation of the spin chains derived from single trace operators in N=6
superconformal Chern-Simons theories. In this paper we give detailed
descriptions of this calculation and the computation of the four-loop wrapping
corrections for a length four operator in the 20 of SU(4), the R-symmetry group
for these theories. Here, we give all relevant Feynman diagrams and loop
integrals explicitly, and also demonstrate the cancellation of double poles in
the logarithm of the renormalization constant.
