One-loop aspects of de Sitter axion wormholes

TL;DR

This paper analyzes one-loop quantum effects of de Sitter axion wormholes, including phase calculations, effective descriptions, and stability, providing insights into their quantum properties and dual operator coefficients.

Contribution

It offers a detailed one-loop analysis of de Sitter axion wormholes, including phase computation, effective sphere operator descriptions, and stability assessment of Einstein wormholes.

Findings

The phase of the path integral can be interpreted via the Polchinski phase and operator position fluctuations.

The antipodal operator configuration is shown to be unstable.

The spectrum of fluctuations for Einstein wormholes is analytically determined, confirming known instabilities.

Abstract

We discuss aspects of the Euclidean path integral around axion-supported de Sitter wormholes, at one-loop order. We numerically compute the phase of the path integral around these solutions, as well as for a certain "multiple wormholes" generalization, and interpret this phase in different regimes. When the geometry is well approximated by a sphere with a small handle, the wormhole admits an effective description as a sphere with two local operator insertions, whose positions fluctuate around the antipodal configuration. The antipodal configuration is an extremum of the position integral for the operators, but we show that it is an unstable one. Accordingly, the phase of the wormhole solution can be viewed as the Polchinski phase in the sphere, multiplied by an additional phase from the integral over positions of the effective local operators. Using our expressions for the one-loop determinant, we also estimate the EFT coefficients of the dual bilocal operators in odd spacetime dimensions, to one-loop order. Lastly, we also discuss "maximal flux" solutions, which have $S^{1}\times S^{D-1}$ geometry. Their Lorentzian continuations are Einstein static universes, so we call them "Einstein wormholes". In this limit, we determine the spectrum of fluctuations analytically and show that the phase of the path integral around this solution is entirely accounted for by the well-known instability of the Einstein static universe.