Supermembranes and Superstrings with Extrinsic Curvature

TL;DR

This paper derives world-volume actions for supermembranes and superstrings from solitonic solutions in supergravity, revealing additional curvature terms that may influence their spectra and symmetries.

Contribution

It provides a novel derivation of supermembrane and superstring actions including extrinsic curvature terms from supergravity solitons, maintaining key symmetries.

Findings

World-volume action includes curvature and extrinsic curvature terms.

Spectrum of membranes may become discrete due to curvature terms.

Background metric rescaling preserves kappa-symmetry and conformal invariance.

Abstract

In a recent paper Townsend suggested to associate to the D=11 solitonic membrane of N=1 supergravity a certain thickness, and then to identify this membrane with the fundamental supermembrane. By integrating out the 8 transverse dimensions of the "thick" solitonic membrane, we show that the resulting world-volume action indeed contains all the usual supermembrane terms, as well as background curvature terms and extrinsic curvature terms, which are believed to render the membrane spectrum discrete. We also outline the analog derivation for the "thick" D=10 solitonic string solution of N=IIA supergravity. The resulting world-sheet action contains the usual type IIA superstring terms, as well as extra terms whose presence can be interpreted as a rescaling of the background metric, thus preserving kappa-symmetry and conformal invariance.