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  • Open Access

O(4)-Breaking Bubble

Guy Avraham*, Kfir Blum†, Omri Rosner‡, and Isaac G. Smith§

  • *Contact author: guy.avraham@weizmann.ac.il
  • †Contact author: kfir.blum@weizmann.ac.il
  • ‡Contact author: omri.rosner@weizmann.ac.il
  • §Contact author: isaacsmi@weizmann.ac.il
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Phys. Rev. Lett. 137, 181602 – Published 27 October, 2026

DOI: https://doi.org/10.1103/pxds-lcv1

Abstract

False vacuum decay in scalar field theory is thought to be dominated by Coleman’s O(4)-symmetric bounce, the minimum action nontrivial solution of the imaginary-time equations of motion. Beyond the bounce, nonconstructive existence proofs of O(4)-breaking solutions are available in the mathematics literature, but the solutions themselves, and their physics, have remained unknown. Considering the simple, bounded-below, scalar field potential V(ϕ)=(m2/2)ϕ2−(λ/4)ϕ4+(g/6)ϕ6, we construct a nonradial solution explicitly: two bubble tubes of opposite sign wrapping orthogonal rings, invariant under O(2)×O(2) rotations combined with a Z2 symmetry that exchanges the rings. The solution admits valid Cauchy data for real-time evolution from a t=0 slice, and supports an odd >1 number of unstable deformation modes. Having found this first solution we proceed to discover additional examples, in 3D as well as other 4D theories, including a Z2-violating potential and scalar QED for which there were no previously known existence proofs or O(4)-dominance theorems.

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Phys. Rev. Lett. 137, 181602– Published 27 October, 2026
  • Received 17 June 2026
  • Revised 26 July 2026
  • Accepted 6 October 2026
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