Anomalous radius shift in AdS4/CFT3

We study higher order corrections to the radius/M2-brane charge of AdS(4)xS(7)/Z(k). There are two sources of corrections: one from the orbifold singularity of C-4/Z(k), and the other from the discrete torsion associated with the homology 3-cycle H-3(S-7/Z(k), Z) = Z(k). We give a precise formula for the charge shift. These corrections are relevant, for example, at two loops in the AdS(4)xCP(3) sigma model, and therefore for the strong coupling test of the all loop Bethe ansatz.