Anomalous radius shift in AdS 4/CFT 3

Abstract

We study higher order corrections to the radius/M2-brane charge of AdS 4 × S 7/ℤ k. There are two sources of corrections: one from the orbifold singularity of 4/ℤ k, and the other from the discrete torsion associated with the homology 3-cycle H 3(S 7/ℤ kℤ) = ℤ k. We give a precise formula for the charge shift. These corrections are relevant, for example, at two loops in the AdS 4 × ℂ P 3 sigma model, and therefore for the strong coupling test of the all loop Bethe ansatz. © SISSA 2009.