Quantum Fluctuations and New Instantons I: Linear Unbounded Potential

TL;DR

This paper investigates false vacuum decay with unbounded linear potentials, revealing how quantum fluctuations introduce natural cutoffs that resolve issues with small instantons and lead to new, non-singular instanton solutions.

Contribution

It introduces a new class of $O(4)$ invariant instantons stabilized by quantum fluctuations in unbounded potentials, extending the understanding of vacuum decay beyond classical methods.

Findings

Quantum fluctuations induce ultraviolet and infrared cutoffs.

New non-singular instantons emerge in unbounded linear potentials.

Small instanton problems are resolved by quantum effects.

Abstract

We consider the decay of a false vacuum in circumstances where the methods suggested by Coleman run into difficulties. We find that in these cases quantum fluctuations play a crucial role. Namely, they naturally induce both an ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new $O(4)$ invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. We apply our results to a case where the potential is unbounded from below in a linear way and in particular show how the problem of small instantons is resolved by taking into account the inevitable quantum fluctuations.