Negative Modes of Oscillating Instantons

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.