  We consider the problem of creating locally supersymmetric theories in
signature (10,2). The most natural algebraic starting point is the F-algebra,
which is the de Sitter-type (10,2) extension of the super-Poincare 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 Einstein-type equation in which
a quadratic non-linearity 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 multi-temporal variables and their relation to ultra-hyperbolic wave
equations.
