String-Membrane Duality in Seven Dimensions

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.

The original version of this paper dealt mostly with one side of string-membrane duality: the solitonic interpretation of the heterotic string as a $K_3$ compactified D=11 superfivebrane. The revised version includes a discussion of the converse prediction: that the supermembrane has a solitonic interpretation as a $T^3$ compactified heterotic fivebrane. It also includes a discussion of D=8 membrane-membrane duality, and various changes to the references