Torsional instanton effects in quantum gravity

TL;DR

This paper explores how instanton effects in quantum gravity with axions relate to topological indices, revealing quantization of axion charge and a connection to the Barbero-Immirzi parameter, indicating nonperturbative vacuum structures.

Contribution

It demonstrates that the instanton number in first order gravity with axions corresponds to the Nieh-Yan topological index, linking axion charge quantization to topological invariants.

Findings

Instanton number equals the Nieh-Yan index.

Axion charge of baby universes is quantized.

Topological vacuum angle matches the Barbero-Immirzi parameter.

Abstract

We show that, in the first order gravity theory coupled to axions, the instanton number of the Giddings-Strominger wormhole can be interpreted as the Nieh-Yan topological index. The axion charge of the baby universes is quantized in terms of the Nieh-Yan integers. Tunneling between universes of different Nieh-Yan charges implies a nonperturbative vacuum state. The associated topological vacuum angle can be identified with the Barbero-Immirzi parameter.