Complex Saddles and Euclidean Wormholes in the Lorentzian Path Integral

TL;DR

This paper investigates complex saddle points in the Lorentzian path integral for 4D axion gravity, including Euclidean wormholes, revealing their stability and how their properties change with higher-topology transitions.

Contribution

It introduces a detailed analysis of complex saddles and Euclidean wormholes in Lorentzian quantum gravity, utilizing Picard-Lefschetz theory and exploring their stability.

Findings

Giddings-Strominger wormhole is perturbatively stable.

Number and nature of saddles change with higher-topology operators.

Stability analysis questions the fate of wormholes in UV-complete theories.

Abstract

We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms of a 3-form flux, which include the Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. We also analyze the stability of the Giddings-Strominger wormhole in the 3-form picture, where we find that it represents a perturbatively stable Euclidean saddle of the gravitational path integral. This calls into question the ultimate fate of such solutions in an ultraviolet-complete theory of quantum gravity.