Negative Modes of Oscillating Instantons

TL;DR

This paper analyzes oscillating instanton solutions, revealing that solutions with N nodes have N negative modes, indicating their instability, while single-node solutions have a single negative mode confirming their tunneling role.

Contribution

It provides a detailed spectral analysis of oscillating instantons, clarifying the stability and physical interpretation of solutions with multiple nodes.

Findings

Solutions with N nodes have N negative modes.

Solutions with N > 1 are unstable intermediate states.

Single-node solutions have a single negative mode.

Abstract

We investigate in detail the properties of oscillating instanton solutions discussed recently in the literature. We find that the solutions with N nodes contain exactly N homogeneous negative modes in their spectrum of linear perturbations. The existence of extra negative modes for the N > 1 solutions suggest that they are not final state physical objects resulting from tunneling, but rather unstable intermediate thermal configurations. By contrast, the single negative mode for the N = 1 instanton confirms its interpretation as mediating the curved-space tunneling between vacua with equal energy densities.