Wormholes in Maximal Supergravity
Aaron Bergman, Jacques Distler
TL;DR
This paper extends the search for Euclidean wormhole saddles in maximal supergravity to toroidal compactifications with $d\le 9$, showing that complex wormhole solutions arise from Wick-rotating cyclic scalars on the symmetric-space moduli $\mathcal{M}=G/K$. It provides a general construction via Cartan/Iwasawa decomposition and confirms the approach with an explicit $SL_2(\mathbb{R})/SO(2)$ example. A central claim is that, once the discrete U‑duality group $G(\mathbb{Z})$ is taken into account, these complex saddles cannot be consistently defined as U‑duality invariant objects, preventing their contribution to the quantum gravity path integral. Consequently, the paper generalizes prior results by arguing that wormholes do not modify the path integral in any dimension within this framework.
Abstract
In this brief note, we reconsider the problem of finding Euclidean wormhole solutions to maximal supergravity in d dimensions. We find that such solutions exists for all d less than or equal to 9. However, we argue that, in toroidally-compactified string theories, these saddle points never contribute to the path integral because of a tension with U-duality.