The O(4)-breaking bubble
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, non-constructive 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)=m2/2ϕ2−λ/4ϕ4+g/6ϕ6, 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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BibTeX
@misc{avraham2026o4breaking,
title = {{The O(4)-breaking bubble}},
author = {Guy Avraham and Kfir Blum and Omri Rosner and Isaac G. Smith},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.16024},
eprint = {2606.16024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16024},
note = {CC0},
}
RIS
TY - UNPB
TI - The O(4)-breaking bubble
AU - Guy Avraham
AU - Kfir Blum
AU - Omri Rosner
AU - Isaac G. Smith
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.16024
UR - https://arxiv.org/abs/2606.16024
AB - 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, non-constructive 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)=m^2/2ϕ^2−λ/4ϕ^4+g/6ϕ^6, 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 Z_2 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 Z_2-violating potential and scalar QED for which there were no previously known existence proofs or O(4)-dominance theorems.
ER -