
TL;DR
This paper reduces three-dimensional gravity to a Liouville theory in asymptotic de Sitter spaces, exploring the roles of infinities and the implications for dual theories.
Contribution
It provides a detailed reduction of 3D gravity to Liouville theory with conditions from asymptotic de Sitter spaces, highlighting new space-time profiles.
Findings
Existence of non-equivalent Liouville profiles at past and future infinities
Conditions on Liouville fields imposed by space-time evolution
Implications for dual theories in de Sitter space
Abstract
A careful reduction of the three-dimensional gravity to the Liouville description is performed, where all gauge fixing and on-shell conditions come from the definition of asymptotic de Sitter spaces. The roles of both past and future infinities are discussed and the conditions space-time evolution imposes on both Liouville fields are explicited. Space-times which correspond to non-equivalent profiles of the Liouville field at past and future infinities are shown to exist. The qualitative implications of this for any tentative dual theory are presented.
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