BPS preons, generalized holonomies, andD=11supergravities

Abstract

We develop the BPS preon conjecture to analyze the supersymmetric solutions of D = 11 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 ν = k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (ν = 31/32) solutions of the standard D = 11 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(1|32)-related supergravity model. We discuss the possible implications for M-theory.

Two-twistor description of a membrane

“…The techniques of supersymmetrization of various twistorial p-brane models were already studied (see e. g. [22,23]). It should be also mentioned that our construction can be linked to the analysis based on the use of Lorentz harmonics [19] as well as with the formalism using d = 11 BPS preons [40,41] described by generalized OSp(1|64) supertwistor fields.…”

Twistor transform inddimensions and a unifying role for twistors

“…The supergroup OSp(1|64) is motivated by other considerations as well [20][21] [22]. In other approaches to twistors in D=11 [23] [24], twistors in the fundamental representation of OSp(1|64) were used in [24] for the formulation of a superstring action in an extended D=11 superspace.…”

Expansions of Algebras and Superalgebras and Some Applications

“…The field B a 1 ...a 5 , associated to the Z a 1 ...a 5 M-algebra generator, is needed [51] for a coupling to BPS preons [52], the hypothetical basic constituents of Mtheory. In a more conventional perspective, one can notice that the generators Z a 1 a 2 and Z a 1 ...a 5 can be treated as topological charges [5] of the M2 and M5 superbranes (see also [53]).…”