Timelike-bounded dS4 holography from a solvable sector of the T2 deformation

Abstract

Recent research has leveraged the tractability of TT¯ style deformations to formulate timelike-bounded patches of three-dimensional bulk spacetimes including dS3. This proceeds by breaking the problem into two parts: a solvable theory that captures the most entropic energy bands, and a tuning algorithm to treat additional effects and fine structure. We point out that the method extends readily to higher dimensions, and does not require factorization of the full T2 operator (the higher dimensional analogue of TT¯ defined in [1]). Focusing on dS4, we first define a solvable theory at finite N via a restricted T2 deformation of the CFT3 on S2×R, in which T is replaced by the form it would take in symmetric homogeneous states, containing only diagonal energy density E/V and pressure (-dE/dV) components. This defines a finite-N solvable sector of dS4/deformed-CFT3, capturing the radial geometry and count of the entropically dominant energy band, reproducing the Gibbons-Hawking entropy as a state count. To accurately capture local bulk excitations of dS4 including gravitons, we build a deformation algorithm in direct analogy to the case of dS3 with bulk matter recently proposed in [2]. This starts with an infinitesimal stint of the solvable deformation as a regulator. The full microscopic theory is built by adding renormalized versions of T2 and other operators at each step, defined by matching to bulk local calculations when they apply, including an uplift from AdS4/CFT3 to dS4 (as is available in hyperbolic compactifications of M theory). The details of the bulk-local algorithm depend on the choice of boundary conditions; we summarize the status of these in GR and beyond, illustrating our method for the case of the cylindrical Dirichlet condition which can be UV completed by our finite quantum theory.