In Generalised supersymmetric fluxbranes, we classified all smooth reductions of Minkowski spacetime by the action of ℝ. (There are no free circle actions on Minkowski spacetime.) Furthermore we determined those reductions which preserve supersymmetry and in this way classified the generalised supersymmetric fluxbranes.
Besides the fluxbranes, for which the ℝ-action consists of a rotation and a translation in a normal direction, we also discovered reductions we called nullbranes, for which the ℝ-action consists of a null rotation and a normal translation.
Associated to every ℝ-quotient, there is an associated ℤ-quotient obtained by choosing a nontrivial element γ∈ℝ and considering the subgroup ℤ⊂ℝ it generates. The resulting quotient, if smooth, is locally isometric to the original spacetime, but can have different global properties. In particular, the discrete quotients associated to the nullbranes give rise to time-dependent, supersymmetric cosmologies which interpolate smoothly between a Big Crunch and a Big Bang epochs. Furthermore it is a background which can be treated exactly in conformal field theory, being a ℤ-orbifold of the usual free string theory. This conformal field theory has been studied by Liu, Moore and Seiberg.