Euclidean axion wormholes have multiple negative modes

TL;DR

This paper analyzes Euclidean wormholes in gravity with a single axion and a negative cosmological constant, demonstrating that macroscopic axion wormholes host multiple inhomogeneous negative modes that lower the Euclidean action. By formulating the perturbations in a gauge-invariant variable, the conjugate momentum $\Pi_{\mathcal{X}}$ of the axion-dressed perturbation, and imposing Dirichlet conditions on $\Pi_{\mathcal{X}}$, the authors show that homogeneous modes are absent while inhomogeneous modes ($n>2$) produce negative directions concentrated near the neck, causing these wormholes to be non-saddle points. Consequently, AdS/CFT paradoxes associated with wormholes are alleviated, as the macroscopic solutions are unstable and likely flow to ensembles of microscopic quantum wormholes with unit charge, though such quantum configurations lie beyond the semiclassical regime. The work also notes that dilaton instantons do not exhibit negative modes, highlighting a qualitative distinction between axion and dilaton sectors and pointing to broader implications for shift-symmetry breaking and nonperturbative axion physics.

Abstract

We show that Euclidean axion wormholes in theories of gravity coupled to a single axion have several independent inhomogeneous perturbations that lower the Euclidean action. Our analysis relies on a judiciously chosen gauge-invariant variable which makes the negative mode structure about axion wormholes transparent. Perturbations lowering the action are concentrated in the neck region and exist for wormholes in flat space and in AdS. Their presence means axion wormholes are not relevant saddle points of the functional integral in quantum gravity. This resolves the paradoxes associated with these solutions from the viewpoint of AdS/CFT. We conjecture that the lower action configurations one flows to are ensembles of microscopic `quantum wormholes' with unit charge.

Figures (1)

• Figure 1: The coefficients $A_n^{-1}$ (blue) and $B_n^{-1}$ (orange) entering in the action for perturbations about axion wormholes, shown here for $n=3$ (and with $c=1$).