Large N Phases, Gravitational Instantons and the Nuts and Bolts of AdS Holography

TL;DR

This paper explores the thermodynamics of quantum gravity in asymptotically AdS spaces, demonstrating a correspondence with large N quantum field theory, and analyzes phase structures of specific spacetimes like AdS-Taub-NUT and AdS-Taub-Bolt.

Contribution

It provides explicit calculations of thermodynamic phases for locally asymptotic AdS spacetimes and compares them with dual conformal field theories, extending holographic correspondence.

Findings

Thermodynamics of AdS-Taub-NUT and AdS-Taub-Bolt spacetimes match large N CFT predictions.

Evidence for unitary evolution in quantum gravity processes including topology change.

Phase structures are consistent with holographic duality even for locally asymptotically AdS spaces.

Abstract

Recent results in the literature concerning holography indicate that the thermodynamics of quantum gravity (at least with a negative cosmological constant) can be modeled by the large N thermodynamics of quantum field theory. We emphasize that this suggests a completely unitary evolution of processes in quantum gravity, including black hole formation and decay; and even more extreme examples involving topology change. As concrete examples which show that this correspondence holds even when the space-time is only locally asymptotically AdS, we compute the thermodynamical phase structure of the AdS-Taub-NUT and AdS-Taub-Bolt spacetimes, and compare them to a 2+1 dimensional conformal field theory (at large N) compactified on a squashed three sphere, and on the twisted plane.