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

TL;DR

This paper explores the theoretical framework of membranes at the end of the universe in various spacetime signatures, focusing on their holographic duals and supersymmetry constraints, especially in de Sitter space contexts.

Contribution

It generalizes the concept of the membrane at the universe's end to diverse signatures and links these to holographic duals in de Sitter space, expanding the understanding of M-branes and superconformal theories.

Findings

Identifies supersymmetry restrictions on membrane signatures.

Connects doubly holographic geometries to M-brane configurations.

Relates de Sitter holography to M-theory brane limits.

Abstract

The original {\it membrane at the end of the universe} corresponds to a probe $M2$-brane of signature $(2,1)$ occupying the $S^{2} \times S^{1}$ boundary of the $(10,1)$ spacetime $AdS_{4} \times S^{7}$, 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 $dS_{4}$ 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 $O(s+1,t+1) \times O(S-s,T-t)$ be a subgroup of a superconformal group. The case of $dS_{4} \times AdS_{7}$ is `doubly holographic' and may be regarded as the near horizon geometry of $N_{2}$ $M2$-branes or equivalently, under interchange of conformal and R symmetry, of $N_{5}$ $M5$-branes, provided $N_{2}=2N_{5}{}^{2}$. The same correspondence holds in the pp-wave limit of conventional $M$-theory.