The membrane at the end of the (de Sitter) universe

The original membrane at the end of the universe corresponds to a probe M2-brane of signature (2,1) occupying the S2×S1 boundary of the (10,1) spacetime AdS4×S7, and is described by an OSp(4/8) SCFT. However, it was subsequently generalized to other worldvolume signatures (s,t) and other spacetime signatures (S,T). An interesting special case is provided by the (3,0) brane at the end of the de Sitter universe dS4 which has recently featured in the dS/CFT correspondence. The resulting CFT contains the one recently proposed as the holographic dual of a four-dimensional de Sitter cosmology. Supersymmetry restricts S, T, s, t by requiring that the corresponding bosonic symmetry O(s+1,t+1)×O(S−s,T−t) be a subgroup of a superconformal group. The case of dS4×AdS7 is 'doubly holographic' and may be regarded as the near horizon geometry of N2 M2-branes or equivalently, under interchange of conformal and R-symmetry, of N5 M5-branes, provided N2=2N52. The same correspondence holds in the pp-wave limit of conventional M-theory.