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dS/dS and $T\bar T$

Victor Gorbenko, Eva Silverstein, Gonzalo Torroba

TL;DR

The paper addresses constructing a holographic description of de Sitter space by generalizing the $T\bar{T}$ deformation to build a patch of bulk $dS_3$ and coupling it to a 2d cosmological constant. On the gravity side, it derives a generalized trace flow equation and analyzes the dS ground state, higher-energy dressings, perturbation propagation, and bulk reconstruction, revealing how a simple boundary flow captures the warped throat geometry. On the 2d field theory side, it defines a two-stage trajectory in the space of theories, introducing a $\Lambda_2$-flow alongside $T\bar{T}$ to reproduce the bulk data, and provides a concrete parameter dictionary in the large-$c$ limit. The paper also computes holographic and DS/dS/dS entanglement entropies, finding precise agreement and highlighting how de Sitter features emerge from a seed AdS/CFT framework, suggesting a mechanism to obtain de Sitter solutions from AdS seeds.

Abstract

The $T\bar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead. At each step along the trajectory in the space of $2d$ theories, the theory is deformed by a specific combination of $T\bar T$ and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.

dS/dS and $T\bar T$

TL;DR

The paper addresses constructing a holographic description of de Sitter space by generalizing the deformation to build a patch of bulk and coupling it to a 2d cosmological constant. On the gravity side, it derives a generalized trace flow equation and analyzes the dS ground state, higher-energy dressings, perturbation propagation, and bulk reconstruction, revealing how a simple boundary flow captures the warped throat geometry. On the 2d field theory side, it defines a two-stage trajectory in the space of theories, introducing a -flow alongside to reproduce the bulk data, and provides a concrete parameter dictionary in the large- limit. The paper also computes holographic and DS/dS/dS entanglement entropies, finding precise agreement and highlighting how de Sitter features emerge from a seed AdS/CFT framework, suggesting a mechanism to obtain de Sitter solutions from AdS seeds.

Abstract

The deformation of a conformal field theory has a dual description as a cutoff spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk spacetime instead. At each step along the trajectory in the space of theories, the theory is deformed by a specific combination of and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.

Paper Structure

This paper contains 19 sections, 92 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Trajectory from the (A)$dS_3$ bulk
  3. The trace flow equation
  4. Solution for the dS ground state
  5. The dressing of higher energy levels
  6. Luminality of the perturbations
  7. Reconstructing the bulk geometry
  8. $T \bar{T}$ and $\Lambda_2$ flow in the $2d$ dual
  9. Defining the $2d$ trajectory
  10. Relations among parameters and large-$c$ physics
  11. Comments on energy scales and the regime $r<\ell$
  12. Comment on more general configurations
  13. Entanglement entropy
  14. Holographic entanglement entropy
  15. Entanglement entropy in the $dS_2$ dual: DS/dS/dS
  16. ...and 4 more sections

Figures (2)

  • Figure 1: The reconstruction of the $dS/dS$ throat from a seed CFT proceeds via two joined trajectories as described in the text. The first trajectory (on the left) evolves the system from a pure CFT, via a sequence of cutoff AdS/dS systems, to the limit where this cutoff scale goes to zero, indicated by the point at the top of the figure. That point is the start of a new trajectory incorporating $\Lambda_2\propto \eta-1$, with increasing cutoff scale, culminating in the full $dS/dS$ warped throat.
  • Figure 2: Function $C(r)/c$ for different $dS_2$ radii $r$. The black line corresponds to $AdS_3$, and the blue line is for $dS_3$. In the second case, $C(r)$ diverges at $r=\sqrt{\lambda c/12}$.