# Fuzzy Euclidean wormholes in anti-de Sitter space

## TL;DR

This paper explores Euclidean wormholes in anti-de Sitter space created by fuzzy instantons, analyzing their properties, probabilities, and implications for stability and unitarity in a gravitational setting with scalar fields.

## Contribution

It introduces the concept of fuzzy instantons in Euclidean wormholes within AdS space and examines how scalar field potentials influence their formation and properties.

## Key findings

- Massless scalar fields lead to wormholes with decreasing probability as throat size increases.
- Non-trivial potentials require tuning to achieve non-zero tunneling rates.
- Adding mass can produce instant wormholes that collapse to event horizons.

## Abstract

This paper is devoted to an investigation of Euclidean wormholes made by fuzzy instantons. We investigate the Euclidean path integral in anti-de Sitter space. In Einstein gravity, we introduce a scalar field with a potential. Because of the analyticity, there is a contribution of complex-valued instantons, so-called fuzzy instantons. If we have a massless scalar field, then we obtain Euclidean wormholes, where the probabilities become smaller and smaller as the size of the throat becomes larger and larger. If we introduce a non-trivial potential, then in order to obtain a non-zero tunneling rate, we need to tune the shape of the potential. With the $O(4)$ symmetry, after the analytic continuation to the Lorentzian time, the wormhole throat should expand to infinity. However, by adding mass, one may obtain an instant wormhole that should eventually collapse to the event horizon. The existence of Euclidean wormholes is related to the stability or unitarity issues of anti-de Sitter space. We are not conclusive yet, but we carefully comment on these physical problems.