Hologravity

TL;DR

The paper develops the UV extension of the dS/dS holographic duality by performing bulk gravitational calculations in $d$ dimensions and translating them into a dual $d-1$ dimensional gravity+matter framework via a conformal AdS map. It demonstrates that in the UV regime the dual theory exhibits a vanishing total central charge and gravitationally dressed operator dimensions, consistent with two CFTs coupled to gravity and with no Weyl anomaly. The analysis includes finite-temperature behavior and black-brane solutions, revealing a zero heat capacity and a conformal anomaly cancellation, and it connects these results to a Black Hole/Black Hole correspondence that encodes quantum corrections in the dual. The framework is then extended to time-dependent cosmological scenarios, interpreting inflation, reheating, and density perturbations as a time-dependent RG flow and non-equilibrium dynamics in the dual theory, with potential applications to observables in de Sitter space and to other spacetimes like inflationary and landscape backgrounds.

Abstract

The dS/dS correspondence provides a holographic description of quantum gravity in d dimensional de Sitter space near the horizon of a causal region in a well defined approximation scheme; it is equivalent to the low energy limit of conformal field theory on de Sitter space in d-1 dimensions coupled to d-1 dimensional gravity. In this work, we extend the duality to higher energy scales by performing calculations of various basic physical quantities sensitive to the UV region of the geometry near the center of the causal patch. In the regime of energies below the d dimensional Planck scale but above the curvature scale of the geometry, these calculations encode the physics of the d-1 dimensional matter plus gravity system above the crossover scale where gravitational effects become strong. They exhibit phenomena familiar from studies of two dimensional gravity coupled to conformal field theory, including the cancellation of the total Weyl anomaly in d-1 dimensions. We also outline how the correspondence can be used to address the issue of observables in de Sitter space, and generalize the correspondence to other space times, such as black holes, inflationary universes, and landscape bubble decays. In the cases with changing cosmological constant, we obtain a dual description in terms of renormalization group flow.

Figures (4)

• Figure 1: The hierarchy of scales. M$_{d-1}^{d-3}$ =L M$_d^{d-2}$ appears as an induced scale beyond M$_d$, the ultimate cutoff of the theory.
• Figure 2: The position dependent AdS masses in $d=5$ for various values of $M$ and $\xi$.
• Figure 3: The bulk black hole appears as a quantum corrected brane black hole.
• Figure 4: Penrose diagram and spatial slice of inflationary spacetime in the causal patch.