Negative modes and decay-rate transition

TL;DR

This paper explores how negative modes around periodic instanton solutions relate to decay-rate transitions, providing criteria to distinguish first- and second-order transitions based on negative mode behavior.

Contribution

It introduces a method to analyze negative modes to determine the order of decay-rate transitions in instanton solutions.

Findings

First-order transitions show an additional negative mode at high energy.

Second-order transitions maintain a single negative mode across energies.

A criterion for identifying transition order based on negative mode analysis.

Abstract

We investigate a relationship between the number of the negative modes around periodic instanton solution and the type of the decay-rate transition. It is shown that for the case of first-order decay-rate transition the lowest positive mode at low energy periodic instanton becomes additional negative mode at high energy regime, while in the second-order case there is only one negative mode in the full range of energy. This kind of analysis on the negative modes makes it possible to derive the criterion for the first-order transition.