Localisation of the M2-brane

Abstract: We study quantum M2-branes in holographic backgrounds and show that their moduli spaces of zero-modes are localised according to an R-symmetry Killing vector. We discuss the relation with recent results in the context of equivariant localisation in gauged supergravity and argue its origin within M-theory path integrals expanded in saddle points over M2-branes. We argue that the M2-brane partition function, including its non-perturbative corrections, should be compared to the field theory grand canonical partition function. Our results extend recent observations in the context of the giant graviton expansion of superconformal indices to generic supersymmetric AdS boundary conditions. As a byproduct we predict non-perturbative corrections to a variety of supersymmetric observables of the ABJM theory.