Tunneling in Theories with Many Fields

TL;DR

This paper investigates the decay rates of metastable vacua in theories with many scalar fields, revealing how the minimal bounce action scales with the number of fields and challenging previous assumptions.

Contribution

It provides a new understanding of how the minimal bounce action scales with the number of fields in a random potential landscape, correcting prior misconceptions.

Findings

Minimal bounce action scales differently with N than previously thought.

The analysis applies to models with N scalar fields and random potentials.

Extensions to more realistic landscape models are discussed.

Abstract

The possibility of a landscape of metastable vacua raises the question of what fraction of vacua are truly long lived. Naively any would-be vacuum state has many nearby decay paths, and all possible decays must be suppressed. An interesting model of this phenomena consists of $N$ scalars with a random potential of fourth order. Here we show that the scaling of the typical minimal bounce action with $N$ is readily understood, and differs from statements in the literature. We discuss the extension to more realistic landscape models.