Go with the flow(s): radial de Sitter holography and $T^2 (+ Λ_2)$

Abstract

What can we learn about a putative dual to de Sitter spacetime from the bulk? Conversely, what can a candidate dual theory teach us about the bulk? In this work, we construct midisuperspace Wheeler-DeWitt states that are localised on the Schwarzschild-de Sitter spacetime. Using these states, we construct a slice-independent worldtube holographic framework in the static patch. We then construct a dictionary between this worldtube proposal and both the $T^2$ and $T^2 + Λ_2$ frameworks for cut-off holography. In doing so, we provide a bulk realisation of $T^2+ Λ_2$ for dS$_4$ black holes. We identify the average Hamiltonian of our worldtube proposal as the seed energy of the $T^2 (+ Λ_2)$ theories. To recover the $T^2 (+ Λ_2)$ energy spectrum as the average Hamiltonian of a worldtube theory, one must make the bulk framework slice-dependent, and we discuss the consequences of this trade-off.