Bulk-local dS$_3$ holography: the Matter with $T\bar T+\Lambda_2$

TL;DR

This paper develops a duality framework for large-radius 3d de Sitter space using a generalized $T\bar T+\Lambda_2$ deformation, enabling microstate counting and consistent boundary conditions for bulk matter fields.

Contribution

It introduces an algorithm to construct a concrete dual for 3d de Sitter space with matter, generalizing the $T\bar T+\Lambda_2$ deformation to include matter effects and boundary conditions.

Findings

Validates the microstate count for large-radius $dS_3$ holography.

Provides a scheme for defining double-trace operators for deformed boundary conditions.

Embeds matter effects into the $T\bar T+\Lambda_2$ framework, maintaining bulk locality.

Abstract

We propose an algorithm which builds a concrete dual for large-radius 3d de Sitter with a timelike York boundary for both gravity and bulk effective fields. This generalizes the solvable $T\bar T+\Lambda_2$ deformation, whose finite real spectrum accounts for the refined Gibbons-Hawking entropy as a microstate count while reproducing the radial static patch geometry. The required generalization to produce approximately local boundary conditions for bulk quantum fields requires a scheme for defining double-trace operators dual to deformed boundary conditions to realize the finite timelike boundary, valid at finite N. By starting with a small stint of a pure $T\bar T$ trajectory, the theory becomes finite, enabling well-defined subtractions to define the double-trace deformation so as to match the large-N prescription of Hartman, Kruthoff, Shaghoulian, and Tajdini to good approximation. We incorporate the matter effecting an uplift from negative to positive cosmological constant, and analyze the effect of matter on the energy spectrum of the theory arising from time-dependent bulk excitations. This validates the cosmic horizon $dS_3$ microstate count for large-radius $dS_3$ holography, embedding $T\bar T+\Lambda_2$ concretely into a larger theory consistent with bulk locality for matter fields. We comment briefly on potential upgrades to four dimensions and other future directions.