Holography For a De Sitter-Esque Geometry

TL;DR

This work investigates holography in warped de Sitter space (warped dS$_3$) within topologically massive gravity with a positive cosmological constant, revealing a two-horizon geometry whose cosmological entropy can grow without bound. It identifies an asymptotic symmetry group at future infinity comprising a Virasoro algebra and a $\widehat{u(1)}$ current algebra, and derives a right-moving central charge $c_R$ while leaving the left-moving central charge $c_L$ to be fixed by a potential Sugawara construction. The authors conjecture a dual two-dimensional CFT with central charges $c_L$ and $c_R$ that reproduces the cosmological-horizon entropy via a Cardy-like formula and discuss a mass gap $\Delta E_R = -c_R/(24\ell)$, signaling a holographic relation between warped dS$_3$ and a CFT. They also explore thermodynamics, the Nariai limit, boundary conditions, and instanton-mediated processes, highlighting both promising evidence for dS holography and key open questions about unitarity and microscopic duals.

Abstract

Warped dS$_3$ arises as a solution to topologically massive gravity (TMG) with positive cosmological constant $+1/\ell^2$ and Chern-Simons coefficient $1/μ$ in the region $μ^2 \ell^2 < 27$. It is given by a real line fibration over two-dimensional de Sitter space and is equivalent to the rotating Nariai geometry at fixed polar angle. We study the thermodynamic and asymptotic structure of a family of geometries with warped dS$_3$ asymptotics. Interestingly, these solutions have both a cosmological horizon and an internal one, and their entropy is unbounded from above unlike black holes in regular de Sitter space. The asymptotic symmetry group resides at future infinity and is given by a semi-direct product of a Virasoro algebra and a current algebra. The right moving central charge vanishes when $μ^2 \ell^2 = 27/5$. We discuss the possible holographic interpretation of these de Sitter-esque spacetimes.

Figures (1)

• Figure 1: Penrose diagram of dS$_2$. There are cosmological horizons at $r^2 = 1$. Future and past infinity lie at $\mathcal{I}^\pm$ and the left and right edges are identified. The static patch covers anyone of the diamonds, whereas the global patch covers the whole diagram.