Kavli Affiliate: Misao Sasaki
| First 5 Authors: Misao Sasaki, Vicharit Yingcharoenrat, Ying-li Zhang, ,
| Summary:
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.
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