Constrained instantons in scalar field theories
File(s)
Published version
Author(s)
Elder, Benjamin
Gawrych, Kinga
Rajantie, Arttu
Type
Journal Article
Abstract
Instantons, localised saddle points of the action, play an important role in describing non-perturbative aspects of quantum field theories, for example vacuum decay or violation of conservation laws associated with anomalous symmetries. However, there are theories in which no saddle point exists. In this paper, we revisit the idea of constrained instantons, proposed initially by Affleck in 1981, and develop it into a complete method for computing the vacuum decay rate in such cases. We apply this approach to the massive scalar field theory with a negative quartic self-interaction using two different constraints. We solve the field equations numerically and find a two-branch structure, with two distinct solutions for each value of the constraint. By counting the negative modes, we identify one branch of solutions as the constrained instantons and the other as the minima of the action subject to the constraint. We discuss their significance for the computation of the vacuum decay rate.
Date Issued
2026-04-01
Date Acceptance
2026-02-11
Citation
Journal of High Energy Physics (JHEP), 2026, 2026 (4)
ISSN
1126-6708
Publisher
SpringerOpen
Journal / Book Title
Journal of High Energy Physics (JHEP)
Volume
2026
Issue
4
Copyright Statement
© The Authors. Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
License URL
Publication Status
Published
Article Number
17
Date Publish Online
2026-04-01