Lifetimes of (near) eternal false vacua

TL;DR

This paper explores long-lived false vacua in quantum field theories protected by higher-form symmetries, analyzing their lifetimes and symmetry structures in 2D abelian gauge theories and 4D QCD.

Contribution

It introduces a mechanism where false vacua are stabilized by $(d-1)$-form global symmetries and studies their properties in specific gauge theories, revealing a higher-group symmetry structure.

Findings

False vacua lifetimes can be parametrically long despite large energy differences.

Modification of instanton sums leads to higher-group symmetries in 4D QCD.

Near-eternal false vacua are realized in 2D abelian gauge theories and 4D QCD.

Abstract

We consider examples of long-lived false vacua in quantum field theory that arise from so-called `universes'. These false vacua are protected by a $(d-1)$-form global symmetry, where $d$ is the dimension of spacetime. The lifetimes of the false vacua are set by UV data: the tension of $(d-2)$-branes charged under a $(d-2)$-form gauge symmetry. The lifetimes can be made parametrically long even when the difference in energy density between the false and true vacua is large compared to the natural scales of the field theory. We study examples of near-eternal false vacua in abelian gauge theories in two dimensions and in four-dimensional QCD. In both cases, it is possible to view the $(d-1)$-form symmetries as arising from a modification of the sum over instantons. We find that the modification of the instanton sum in 4d QCD leads to a higher-group symmetry structure involving the 3-form and conventional 0-form global symmetries.