Quantum Dynamics of Supergravity on R^3 x S^1

TL;DR

This paper investigates the quantum behavior of N=1 supergravity on a compact circle, revealing that instanton effects destabilize supersymmetric compactification, leading to decompactification and uncovering a new infra-red scale linked to gravitational instantons.

Contribution

It demonstrates how instanton effects cause supersymmetric compactification to become unstable, introducing a novel infra-red scale from the logarithmic running of the Gauss-Bonnet term.

Findings

Supersymmetry cancels perturbative Casimir energy contributions.

Instantons induce decompactification of the circle.

A new infra-red scale emerges from gravitational instantons.

Abstract

We study the quantum dynamics of N=1 supergravity in four dimensions with a compact spatial circle. Supersymmetry ensures that the perturbative contributions to the Casimir energy on the circle cancel. However, instanton contributions remain. These render supersymmetric compactification on a circle unstable and the background dynamically decompactifies back to four dimensions. The calculation provides a testing ground for some old ideas in Euclidean quantum gravity. In particular, we show that gravitational instantons are associated to a new, infra-red scale which is naturally exponentially suppressed relative to the Planck scale and arises from the logarithmic running of the Gauss-Bonnet term. There are also some interesting technical details, including the non-cancellation of bosonic and fermionic determinants around the background of a self-dual gravitational instanton, despite the existence of supersymmetry.