Anomalous radius shift in AdS4/CFT3

Abstract

We study higher order corrections to the radius/M2-brane charge of AdS4 ×S 7 /Zk. There are two sources of corrections: one from the orbifold singularity of C 4 /Zk, and the other from the discrete torsion associated with the homology 3-cycle H3(S 7 /Zk, Z) = Zk. We give a precise formula for the charge shift. These corrections are relevant, for example, at two loops in the AdS4 × CP 3 sigma model, and therefore for the strong coupling test of the all loop Bethe ansatz.