2024/11/18 by Misao Sasaki, Sasaki, Misao, Vicharit Yingcharoenrat +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2411.11322
openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the absence of gravity, Coleman's theorem states that the O(4)-symmetric instanton solution, which is regular at the origin and exponentially decays at infinity, gives the lowest action. Perturbatively, this implies that any small deformation from O(4)-symmetry gives a larger action. In this letter we investigate the possibility of extending this theorem to the situation where the O(4)-symmetric instanton is singular, provided that the action is finite. In particular, we show a general form of the potential around the origin, which realizes a singular instanton with finite action. We then discuss a concrete example in which this situation is realized, and analyze non-trivial anisotropic deformations around the solution perturbatively. Intriguingly, in contrast to the case of Coleman's instantons, we find that there exists a deformed solution that has the same action as the one for the O(4)-symmetric solution up to the second order in perturbation. Our result implies that there exist non-O(4)-symmetric solutions with finite action beyond Coleman's instantons, and gives rise to the possibility of the existence of a non-O(4)-symmetric instanton with a lower action.