String-Membrane Duality in Seven Dimensions

TL;DR

This paper explores a duality between strings and membranes in seven dimensions, deriving it from known string dualities and verifying the relationship through compactification of worldvolume actions.

Contribution

It introduces a novel string-membrane duality in seven dimensions based on heterotic string and supermembrane equivalences, with explicit verification via compactification.

Findings

Heterotic string as a $K_3$ compactification of the fivebrane

Verification of the heterotic string worldsheet action from fivebrane action

Discussion of generalizations to higher dimensions and dualities

Abstract

The conjectured equivalence of the heterotic string to a $K_3$ compactified type IIA superstring is combined with the conjectured equivalence of the latter to a compactified 11-dimensional supermembrane to derive a string membrane duality in seven dimensions; the membrane is a soliton of the string theory and vice versa. A prediction of this duality is that the heterotic string is a $K_3$ compactification of the solitonic 11-dimensional fivebrane. It is verified that the worldsheet action of the D=10 heterotic string is indeed obtainable by $K_3$ compactification of the worldvolume action of the 11-dimensional fivebrane, and it is suggested how the worldvolume action of the D=11 supermebrane may be similarly obtained by $T^3$ compactification of the worldvolume action of a D=10 heterotic fivebrane. Generalizations to $D=8$ string-threebrane and membrane-membrane duality are also discussed.