Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Two dimensional de-Sitter and deformed CFTs

Suchetan Das

TL;DR

The paper develops a two-dimensional dilaton gravity framework arising from S-wave reductions of higher-dimensional de Sitter spacetimes, revealing free massless dilatons in the near-Nariai static patch and dynamical dilatons in the past Milne wedge. It proposes a worldsheet description via SL(2,R) deformed CFTs on a cylinder/ring, with a stretched horizon acting as a gravitating observer and with emergent notions of worldsheet time. The Milne-patch dynamics are interpreted as a critical quench, while the static patch is explored through modular quantization and a deformed CFT on a ring that yields an emergent Virasoro algebra and observer entropy. Overall, the work proposes a UV completion in terms of deformed CFTs that encode near-horizon/dS physics and offers a novel perspective on observer time and static patch holography.

Abstract

We present an alternative dimensional reduction that yields an effective theory of dilatons in a two-dimensional de Sitter background. Specifically, by performing an S-wave reduction of higher-dimensional Einstein gravity, we obtain free massless dilatons in the Nariai static patch, and a dynamically evolving dilatons in the past Milne wedge. We then propose a (Nariai) static patch worldsheet formulation in terms of CFTs with SL(2,$\mathbb{R}$) deformed Hamiltonians on the cylinder. A key feature of this construction is that a stretched horizon in the (Nariai) static patch, equipped with an emergent UV boundary condition, acts as a gravitating observer. Using the similar reduction, we have also obtained a Schwarzian action coupled to free massless dilatons in the near horizon near extremal limit of four dimensional charged AdS black holes. The worldsheet description for the same has been proposed and discussed in \cite{Das:2025cuq}. We also comment on how different notions of worldsheet time may themselves be \textit{emergent}.

Two dimensional de-Sitter and deformed CFTs

TL;DR

The paper develops a two-dimensional dilaton gravity framework arising from S-wave reductions of higher-dimensional de Sitter spacetimes, revealing free massless dilatons in the near-Nariai static patch and dynamical dilatons in the past Milne wedge. It proposes a worldsheet description via SL(2,R) deformed CFTs on a cylinder/ring, with a stretched horizon acting as a gravitating observer and with emergent notions of worldsheet time. The Milne-patch dynamics are interpreted as a critical quench, while the static patch is explored through modular quantization and a deformed CFT on a ring that yields an emergent Virasoro algebra and observer entropy. Overall, the work proposes a UV completion in terms of deformed CFTs that encode near-horizon/dS physics and offers a novel perspective on observer time and static patch holography.

Abstract

We present an alternative dimensional reduction that yields an effective theory of dilatons in a two-dimensional de Sitter background. Specifically, by performing an S-wave reduction of higher-dimensional Einstein gravity, we obtain free massless dilatons in the Nariai static patch, and a dynamically evolving dilatons in the past Milne wedge. We then propose a (Nariai) static patch worldsheet formulation in terms of CFTs with SL(2,) deformed Hamiltonians on the cylinder. A key feature of this construction is that a stretched horizon in the (Nariai) static patch, equipped with an emergent UV boundary condition, acts as a gravitating observer. Using the similar reduction, we have also obtained a Schwarzian action coupled to free massless dilatons in the near horizon near extremal limit of four dimensional charged AdS black holes. The worldsheet description for the same has been proposed and discussed in \cite{Das:2025cuq}. We also comment on how different notions of worldsheet time may themselves be \textit{emergent}.

Paper Structure

This paper contains 14 sections, 124 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dimensional Reduction to 2D de-Sitter in near-Nariai limit
  3. Alternative dual reduction in the near-Nariai limit
  4. Partition function of massless free scalar fields in a static patch background with stretched horizon
  5. Dimensional reduction to 2D de-Sitter from Einstein gravity in pure dS$_{D\geq 3}$
  6. Deformed CFT, Milne patch and critical quench
  7. Boundary non-preserving deformed CFT Hamiltonian on a strip and Milne patch dynamics
  8. Emergence of steady state at late time
  9. Deformed CFT, static patch and observer's entropy
  10. Deformed CFT on a ring, emergent Virasoro algebra and stretched horizon in static patch
  11. Modular quantization on static patch and thermal partition function
  12. Discussion
  13. Comment on emergence of observer time
  14. JT gravity and deformed CFT from dimensional reduction of near extremal black holes in near horizon limit

Figures (2)

  • Figure 1: Curves of $\gamma\theta$ and $\gamma s_{E}$ on the UHP($t,x$)
  • Figure 2: Curves of $\theta$ and $t'$ on the full complex plane