Beyond Coleman's Instantons
Nov 18, 2024
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Abstract: (arXiv)
In the absence of gravity, Coleman's theorem states that the -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 -symmetry gives a larger action. In this letter we investigate the possibility of extending this theorem to the situation where the -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 -symmetric solution up to the second order in perturbation. Our result implies that there exist non--symmetric solutions with finite action beyond Coleman's instantons, and gives rise to the possibility of the existence of a non--symmetric instanton with a lower action.Note:
- 6 pages, 3 figures. Corrected error and added references
References(25)
Figures(3)
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