We develop the BPS (Bogomol’nyi-Prasad-Sommerfield) preon conjecture to analyze the supersymmetric solutions of $D=11\mathrm{}$ supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method $[G=GL(32,R),$ $SL(32,R)$ or $Sp(32,R)]$ to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of $\nu =k/32\mathrm{}$ supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic $(\nu =31/32)$ solutions of the standard $D=11\mathrm{}$ supergravity. We also show that there exist elementary preonic solutions, i.e., solutions preserving 31 out of 32 supersymmetries in a Chern-Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D’Auria-Fré type $OSp\left(1\mathrm{}|32\right)$-related supergravity model. We discuss the possible implications for M theory.

• Received 23 December 2003

DOI:https://doi.org/10.1103/PhysRevD.69.105010