Elliptic de Sitter space: [Formula Presented]

Maulik Parikh, Ivo Savonije, Erik Verlinde

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

We propose that, for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an “elliptic” [Formula Presented] identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analogue of an S matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite dimensional and still have a positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type [Formula Presented] string theory.

Original languageEnglish (US)
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume67
Issue number6
DOIs
StatePublished - Jan 1 2003
Externally publishedYes

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matrices
antipodes
subgroups
Hilbert space
norms
string theory
analogs
gravitation

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

Cite this

Elliptic de Sitter space : [Formula Presented]. / Parikh, Maulik; Savonije, Ivo; Verlinde, Erik.

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 67, No. 6, 01.01.2003.

Research output: Contribution to journalArticle

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