De Sitter Space in Supergravity and M Theory

TL;DR

This paper explores how de Sitter space appears in supergravity and M-theory through different solutions, including non-supersymmetric and supersymmetric cases, and discusses their implications for holography and dualities.

Contribution

It reviews and generalizes previous results on de Sitter solutions in supergravity, including unconventional theories and their M-theory origins, with a focus on holography and dualities.

Findings

De Sitter space can be a solution in conventional supergravity without Killing spinors.

Unconventional supergravity theories can admit supersymmetric de Sitter solutions.

Brane solutions connect these vacua to flat space and suggest holographic dualities.

Abstract

Two ways in which de Sitter space can arise in supergravity theories are discussed. In the first, it arises as a solution of a conventional supergravity, in which case it necessarily has no Killing spinors. For example, de Sitter space can arise as a solution of N=8 gauged supergravities in four or five dimensions. These lift to solutions of 11-dimensional supergravity or D=10 IIB supergravity which are warped products of de Sitter space and non-compact spaces of negative curvature. In the second way, de Sitter space can arise as a supersymmetric solution of an unconventional supergravity theory, which typically has some kinetic terms with the `wrong' sign; such solutions are invariant under a de Sitter supergroup. Such solutions lift to supersymmetric solutions of unconventional supergravities in D=10 or D=11, which nonetheless arise as field theory limits of theories that can be obtained from M-theory by timelike T-dualities and related dualities. Brane solutions interpolate between these solutions and flat space and lead to a holographic duality between theories in de Sitter vacua and Euclidean conformal field theories. Previous results are reviewed and generalised, and discussion is included of Kaluza-Klein theory with non-compact internal spaces, brane and cosmological solutions, and holography on de Sitter spaces and product spaces.