On supergravity in (10,2)
Abstract
We consider the problem of creating locally supersymmetric theories in signature (10,2). The most natural algebraic starting point is the Falgebra, which is the de Sittertype (10,2) extension of the superPoincare algebra. We derive the corresponding geometric group curvatures and evaluate the transformations of the associated gauge fields under the action of an infinitesimal group element. We then discuss the formation of locally supersymmetric actions using these quantities. Due to the absence of any vielbein terms there is no obvious way to define spacetime as such. In addition, there is also no way in which we may naturally construct an action which is linear in the twelve dimensional curvatures. We consider the implications of the simplest possible quadratic theories. We then investigate the relationship between the twelve dimensional theories and Lorentz signature theories in lower dimensions. We argue that in this context the process of dimensional reduction must be replaced by that of group theoretic contraction. Upon contraction a regular spacetime emerges and we find that the twelve dimensional curvature constraint reduces to an Einsteintype equation in which a quadratic nonlinearity in the Ricci scalar is suppressed by a factor of the same magnitude as the cosmological constant. Finally, we discuss the degrees of freedom of multitemporal variables and their relation to ultrahyperbolic wave equations.
 Publication:

arXiv eprints
 Pub Date:
 August 1999
 arXiv:
 arXiv:hepth/9908209
 Bibcode:
 1999hep.th....8209H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 12 pages, one reference corrected