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.
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We are grateful to Z. Komargodski, M. Ünsal, and Y. Tanizaki for discussions that inspired this paper. We also thank M. Shifman and A. Vainshtein for lively and clarifying discussions about the Schwinger model, and are very grateful to P. Draper for extensive discussions on the topics in this work and the suggestion to work out a quantum-mechanical example. A. C. is supported by start-up funds from the University of Minnesota. T. J. is supported by a UMN CSE Fellowship.
© 2021 authors. Published by the American Physical Society.