Spinors, superalgebras and the signature of space-time

Abstract

Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension $D\le 11$. These theories are related to $D=11,M,M^{\ast }$ and $M^{\prime }$ theories or $D=10$, IIB, IIB${}^{\ast }$ theories when compactified on Lorentzian tori. All dimensionally reduced theories fall in three distinct phases specified by the number of (128 bosonic) positive and negative norm states: $(n^{+},n^{-})=(128,0),(64,64),(72,56)$.

18 pages, Based on talks given at the ``XIV Sigrav Congress on Recents Developments in General Relativity", Genoa, Italy, September 2000 Workshop on "30 years of Supersymmetry", Minneapolis, U.S.A., October 2000 "Dirac Anniversary Meeting", ICTP, Trieste, Italy, November 2000