Spontaneous compactification in 2D induced quantum gravity

TL;DR

This paper investigates the stability of spontaneous compactification in 2D induced quantum gravity, showing it is stable unlike higher-dimensional cases, using a gauge-independent effective action approach.

Contribution

It demonstrates the stability of spontaneous compactification in 2D induced quantum gravity, contrasting with known instabilities in higher dimensions, via a gauge-independent formalism.

Findings

Spontaneous compactification in 2D gravity is stable.

Higher-dimensional quantum gravity on R^D×S^1 is one-loop unstable.

Gauge-independent effective action formalism is used for analysis.

Abstract

Spontaneous compactification ---on a $R^1\times S^1$ background--- in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a $R^D\times S^1 \ (D>2)$ background ---which is known to be one-loop unstable.