Quantum Gravity: Mixed States from Diffeomorphism Anomalies

TL;DR

This paper explores how anomalies in diffeomorphism symmetries in quantum gravity can lead to mixed states and entropy, potentially relating to black hole entropy.

Contribution

It extends the concept of mixed states from simple models to topological geons in quantum gravity, highlighting the role of anomalies in entropy generation.

Findings

Large diffeomorphisms can become anomalous in quantum gravity.

Mixed states can eliminate these anomalies and generate entropy.

Potential connection between these anomalies and black hole entropy.

Abstract

In a previous paper, we discussed simple examples like particle on a circle and molecules to argue that mixed states can arise from anomalous symmetries. This idea was applied to the breakdown (anomaly) of color SU(3) in the presence of non-abelian monopoles. Such mixed states create entropy as well. In this article, we extend these ideas to the topological geons of Friedman and Sorkin in quantum gravity. The "large diffeos" or mapping class groups can become anomalous in their quantum theory as we show. One way to eliminate these anomalies is to use mixed states, thereby creating entropy. These ideas may have something to do with black hole entropy as we speculate.