Abstract
We study the quantum dynamics of \( \mathcal{N}=1 \) 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.
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Tong, D., Turner, C. Quantum dynamics of supergravity on R3 × S1 . J. High Energ. Phys. 2014, 142 (2014). https://doi.org/10.1007/JHEP12(2014)142
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DOI: https://doi.org/10.1007/JHEP12(2014)142