Constrained instantons in scalar field theories
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914422155378688 |
|---|---|
| author | Elder, Benjamin Gawrych, Kinga Rajantie, Arttu |
| author_facet | Elder, Benjamin Gawrych, Kinga Rajantie, Arttu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constrained instantons in scalar field theories Elder, Benjamin Gawrych, Kinga Rajantie, Arttu High Energy Physics - Theory Mathematical Physics Pattern Formation and Solitons 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. |
| title | Constrained instantons in scalar field theories |
| topic | High Energy Physics - Theory Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2510.21922 |