Kavli Affiliate: Misao Sasaki
| First 5 Authors: Misao Sasaki, Vicharit Yingcharoenrat, Ying-li Zhang, ,
| Summary:
Recently, it was shown that in the absence of gravity there exist
non-$O(4)$-symmetric instanton solutions with finite action beyond Coleman’s
instantons. In this paper, focusing on the false-vacuum decay in a single
scalar field in flat Euclidean space, we provide a general discussion on
$O(4)$-symmetric instantons that are singular at the true-vacuum bubble. We
find that, for the action to remain finite without introducing a UV cutoff, the
potential must be unbounded from below and take the exponential form, thereby
evading Coleman’s theorem. We then consider two explicit examples of such
instantons and perturbatively analyze the dynamics of small deformations around
them. We find that one of them does not allow regular deformations, which
indicates that the $O(4)$ symmetric solution still gives the minimum action,
while the other one is found to allow regular deformations that cost no
additional action at second order in perturbation. The latter example opens up
the possibility of the existence of non-$O(4)$-symmetric solutions with lower
action if we allow singular instantons with finite action.
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