Compactification of Supermembranes

TL;DR

This paper investigates the dimensional reduction of supermembranes in M-theory to D2-branes in Type IIA string theory by analyzing soliton solutions in supergravity, revealing how the eleventh dimension influences the reduction.

Contribution

It introduces a novel approach by focusing on supergravity soliton solutions rather than worldvolume actions for supermembrane compactification.

Findings

Demonstrates the role of the eleventh dimension in the reduction process

Shows how to maintain dependence on the compactification coordinate

Provides insights into the connection between M-theory and Type IIA supergravity

Abstract

We look at the vertical dimensional reduction of the supermembrane of M-theory to the D2-brane of Type IIA string theory. Our approach considers the soliton solutions of the two low energy field limits, D=11 and D=10 Type IIA supergravities, rather than the worldvolume actions. It is thus necessary to create a periodic array. The standard Kaluza-Klein procedure requires that the brane is smeared over a transverse direction, but we will keep the dependence on the compactification coordinate, seeing how the eleventh dimension comes into play when we close up on the D2-brane.