Complex saddles and Euclidean wormholes in the Lorentzian path integral

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.

Axion-de Sitter wormholes

“…Under closer scrutiny our results also reveal that a partitioning of the axion flux does not lower the action, preventing fragmentation into multiple smaller axion wormholes. We also confirm that, for fixed axion flux, these solutions are perturbatively stable, and consistently reproduce the flat space axion wormhole results in the limit of a vanishing cosmological constant [13]. 2 We then study Lorentzian continuations [16] of the wormhole solutions.…”

Axion wormholes with massive dilaton

“…Our results should help clarify the issue of wormhole stability. Note that pure axion wormholes were found to be perturbatively stable [28], despite earlier claims [27]. Still the pertubative stability of wormholes supported by massless axion and dilatons remains unclear, and that situation is directly relevant for the holographic embedding of axion wormholes [38] with all their associated paradoxes [16][17][18].…”

“…Still the pertubative stability of wormholes supported by massless axion and dilatons remains unclear, and that situation is directly relevant for the holographic embedding of axion wormholes [38] with all their associated paradoxes [16][17][18]. On the other hand, setups with massive dilatons are the most relevant for phenomenology, and the stability analysis of [28,39] together with the results of this paper indicate that the wormholes only feature "non-perturbative" instabilities in the sense that wormhole fragmentation will dominate the path integral (see also [19]). What this means for the truly dominating saddle points remains unclear and finding the answer to this question might require an understanding of the full UV completion, not just the leading corrections to the EFT.…”

“…These could indicate that wormholes should not contribute significantly to the path integral. However, recent work [28] has shown that, with the appropriate boundary conditions for the gauge invariant perturbations that keep the axion charge of the wormhole fixed, there are no such negative modes and thus the axion wormhole in [1] is perturbatively stable.…”

Suppression of spacetime singularities in quantum gravity

“…Lorentzian path integrals provide a promising framework for quantum gravity. While methods for the evaluation of highly oscillatory integrals are advancing [23,24,[57][58][59][60][61][62][63][64][65] and there is accumulating evidence that Lorentzian path integrals evade some of the long-standing debates related to the conformal factor problem in Euclidean quantum gravity [66][67][68][69], in this work we have pointed out a further property of Lorentzian path integrals as opposed to their Euclidean counterparts: the prospect for suppression of off-shell spacetime geometries with an unphysical curvature singularity. The suppression mechanism grounds on the observation that whenever the magnitude of the action is large for a set of neighboring singular off-shell geometries in configuration space, the rapidly oscillating phase factor is expected to lead to destructive inteference between these [10][11][12].…”