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

TL;DR

The work identifies and computes higher-order corrections to the radius in AdS_4/CFT_3 for the ABJM setup by evaluating anomalous M2-brane charges associated with the C^4/Z_k orbifold and with discrete torsion. It provides a precise expression for the total M2-charge shift ΔQ_M2 = - (1/24)(k - 1/k) + l^2/(2k) and translates this into a corrected Type IIA radius R_str^2 = 2^{5/2}π√(λ - (1/24)(1 - 1/k^2) + l^2/(2k^2)), with l ∈ {0,...,k-1}. The analysis relies on the I_8 curvature term, G_4 flux, and a constructive description of the relevant 8-manifold M, together with an explicit M and X satisfying X∧X relations. A Type IIA perspective via D-brane domain-wall probes provides a complementary, albeit indirect, check, linking jumps in l and k to induced D2 charges and matching Major contributions to ΔQ_M2. These results imply that radius shifts from higher-order corrections become relevant at two loops in the AdS_4 x CP^3 sigma model and are important for the strong coupling consistency of the all-loop Bethe ansatz in ABJM.

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.