About the Coleman Instantons in D Dimensions

TL;DR

This paper explores the existence of Coleman instantons in various potentials across D-dimensional spacetime, introducing new instantons for certain unbounded potentials and providing exactly solvable models.

Contribution

It identifies classes of unbounded potentials lacking Coleman instantons and constructs exactly solvable potential models in different dimensions.

Findings

Certain unbounded potentials do not admit Coleman instantons.

New instantons are introduced for specific potentials.

Exact solutions for instanton equations are provided in various dimensions.

Abstract

We identify an infinite class of unbounded potentials for which the Coleman instantons do not exist in D-dimensional spacetime. For such potentials, the decay of a false vacuum is described by the new instantons introduced in [5,6,4]. For each spacetime dimension D, we also construct the two different classes of potentials for which the instanton equations are exactly solvable.