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.
Highlights
False vacua are commonplace in quantum field theory (QFT)
The lifetime of the false vacuum decreases as the difference in energy densities between the false and true vacuum is increased
For phenomenological applications of these ideas, one should assume the (d − 2)-branes that are sources for the Zðpd−1Þ symmetry have a finite tension. This tension can be extremely large (Td−2 ∼ MdP−la1nck) compared to the energy scales which are native to our d dimensional QFT, leading to extremely long-lived false vacua, without any need to tune the parameters controlling the low-energy physics
Summary
False vacua are commonplace in quantum field theory (QFT). But we are used to the idea that if we wait long enough, the system always ends up in the true vacuum [1,2,3,4,5,6]. At the point in parameter space where Gð0Þ is a symmetry, the long-distance effective field theory cannot be trivial due to the ’t Hooft anomaly, and in the examples we will discuss Gð0Þ is spontaneously broken, so that there are jGð0Þj degenerate vacua. For phenomenological applications of these ideas, one should assume the (d − 2)-branes that are sources for the Zðpd−1Þ symmetry have a finite tension This tension can be extremely large (Td−2 ∼ MdP−la1nck) compared to the energy scales which are native to our d dimensional QFT, leading to extremely long-lived false vacua, without any need to tune the parameters controlling the low-energy physics. The hierarchy between the scale set by the 2-brane tension T2 and the QCD scale ΛQCD implies that false vacua in the modified QCD theory are very long lived
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