\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
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
gravitational 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.
\end{document}