Anomalous radius shift in AdS(4)/CFT(3)

TL;DR

This paper investigates higher order corrections to the radius and M2-brane charge in AdS_4 x S^7/Z_k, deriving a formula for the charge shift caused by orbifold singularities and discrete torsion, impacting strong coupling tests.

Contribution

It provides a precise formula for the charge shift in AdS_4 x S^7/Z_k due to orbifold singularities and discrete torsion, relevant for higher loop calculations.

Findings

Derived a formula for the charge shift in AdS_4 x S^7/Z_k.

Identified the sources of corrections from orbifold singularity and discrete torsion.

Implications for two-loop corrections in the sigma model and Bethe ansatz tests.

Abstract

We study higher order corrections to the radius/M2-brane charge of AdS_4 x S^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 x CP^3 sigma model, and therefore for the strong coupling test of the all loop Bethe ansatz.