Supermembranes and superstrings with extrinsic curvature

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.