Quantum M2-branes and Holography

TL;DR

This paper explores the semi-classical quantisation of supersymmetric membranes in AdS holographic geometries, revealing ensemble changes, localisation phenomena, and the role of membrane instantons in understanding supergravity data.

Contribution

It introduces a novel analysis of membrane localisation and instanton effects in AdS spaces, linking membrane dynamics to supergravity data extraction.

Findings

Membrane localisation occurs where the background Killing spinor is chiral.

Ensemble changes are necessary when comparing bulk and boundary observables in AdS$_4$ geometries.

Membrane instantons in AdS$_7$ reduce to a quantum mechanical system, supporting the emergence proposal.

Abstract

We discuss the semi-classical quantisation of supersymmetric membranes in holographic geometries with asymptotic AdS$_4$ and AdS$_7$ boundary conditions. In AdS$_4$ geometries this quantisation prompts the need of ensemble changes when comparing bulk and boundary observables arising from such membranes. We also discuss how supersymmetric membranes localise to loci where the background Killing spinor turns chiral, circumventing the need of evaluating their zero-mode moduli integrals. Finally, we discuss a bulk analysis of an infinite tower of membrane instantons, or giant gravitons, in AdS$_7$ geometries, whose worldvolume dynamics effectively reduces to a quantum mechanical system. This allows us to test, in a holographic setting, the emergence proposal that perturbative supergravity data may be extracted from towers of membrane instantons.