Decoding the matrix: Coincident membranes on the plane wave

TL;DR

This paper investigates the holographic encoding of bulk data in matrix models related to quantum gravity, focusing on membrane configurations and their spectra within the plane wave matrix model, revealing key representation theory relations.

Contribution

It identifies and verifies nontrivial representation theory relations that clarify the spectrum inclusion of product states of membranes in the plane wave matrix model.

Findings

Concentric membranes form superselection sectors at large boosts.

Product states of membranes are contained within the full spectrum.

Representation theory relations are crucial for understanding non-BPS state spectra.

Abstract

At the core of nonperturbative theories of quantum gravity lies the holographic encoding of bulk data in large matrices. At present this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation.