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

## TL;DR

This paper constructs a novel two-dimensional geometry called 'centaur' that smoothly connects AdS$_2$ and dS$_2$, providing insights into their thermodynamics and potential dual quantum descriptions.

## Contribution

It introduces the centaur geometry as a solution in dilaton gravity that interpolates between AdS$_2$ and dS$_2$, and analyzes its thermodynamic properties.

## Key findings

- Centaur geometry has finite entropy and positive specific heat.
- Static patch is the infrared limit of the centaur geometry.
- Boundary observables can probe the static patch region.

## 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.