Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Infrared Realization of dS$_2$ in AdS$_2$

Dionysios Anninos, Diego M. Hofman

TL;DR

The paper constructs a centaur geometry—an irreversible interpolation between AdS$_2$ in the UV and dS$_2$ in the IR—within a two-dimensional dilaton gravity framework. By interpreting this geometry as a thermal state in a putative AdS$_2$ quantum-mechanical dual, the authors compute thermodynamics (finite entropy and positive specific heat) and analyze wave propagation and boundary correlators, revealing de Sitter-like IR physics and a distinctive quasinormal spectrum. They further develop explicit sharp-centaur solutions, study worldline correlators in dS$_2$ and higher dimensions, and connect to SYK-like boundary dynamics, highlighting a deconfined yet weakly dissipative regime. The work discusses implications for higher-dimensional generalizations, UV universality, and the pursuit of explicit dual quantum-mechanical models that realize centaur holography.

Abstract

We describe a two-dimensional geometry that smoothly interpolates between an asymptotically AdS$_2$ geometry and the static patch of dS$_2$. We find this `centaur' geometry to be a solution of dilaton gravity with a specific class of potentials for the dilaton. We interpret the centaur geometry as a thermal state in the putative quantum mechanics dual to the AdS$_2$ evolved with the global Hamiltonian. We compute the thermodynamic properties and observe that the centaur state has finite entropy and positive specific heat. The static patch is the infrared part of the centaur geometry. We discuss boundary observables sensitive to the static patch region.

Infrared Realization of dS$_2$ in AdS$_2$

TL;DR

The paper constructs a centaur geometry—an irreversible interpolation between AdS in the UV and dS in the IR—within a two-dimensional dilaton gravity framework. By interpreting this geometry as a thermal state in a putative AdS quantum-mechanical dual, the authors compute thermodynamics (finite entropy and positive specific heat) and analyze wave propagation and boundary correlators, revealing de Sitter-like IR physics and a distinctive quasinormal spectrum. They further develop explicit sharp-centaur solutions, study worldline correlators in dS and higher dimensions, and connect to SYK-like boundary dynamics, highlighting a deconfined yet weakly dissipative regime. The work discusses implications for higher-dimensional generalizations, UV universality, and the pursuit of explicit dual quantum-mechanical models that realize centaur holography.

Abstract

We describe a two-dimensional geometry that smoothly interpolates between an asymptotically AdS geometry and the static patch of dS. We find this `centaur' geometry to be a solution of dilaton gravity with a specific class of potentials for the dilaton. We interpret the centaur geometry as a thermal state in the putative quantum mechanics dual to the AdS evolved with the global Hamiltonian. We compute the thermodynamic properties and observe that the centaur state has finite entropy and positive specific heat. The static patch is the infrared part of the centaur geometry. We discuss boundary observables sensitive to the static patch region.

Paper Structure

This paper contains 29 sections, 76 equations, 3 figures.

Table of Contents

  1. Introduction
  2. UV behavior of QM vs. worldline holography
  3. 'Infinite' quantum mechanics
  4. Conformal quantum mechanics
  5. Finite quantum mechanics?
  6. A/dS$_2$ and the centaur geometry
  7. Static patch dS$_2$ geometry
  8. Global AdS$_2$ geometry
  9. Centaur geometry
  10. Dilaton gravity with centaur vacuum
  11. Centaur thermodynamics
  12. Centaur waves
  13. Wave equation
  14. Exact gluing solution: the sharp centaur
  15. Expectations at $\omega \ell \gg {(2\pi T)^2}/{\ell \epsilon}$
  16. ...and 14 more sections

Figures (3)

  • Figure 1: The Euclidean centaur geometry: a hemisphere merged to the hyperbolic cylinder.
  • Figure 2: Position of quasinormal modes in the complex $\hat{\omega}$-plane for $\mu=1$.
  • Figure 3: Plot of $\sigma(m)/(c \, m^{2\tilde{\Delta}-1})$ vs. $m$ for $\tilde{\Delta} = (1+\sqrt{17})/2 \approx 2.56$. The constant $c$ is chosen such that the curve flattens to one at large $m$.