We compute the vacuum polarization energies (VPEs) of solitons in a self-dual impurity model in which the soliton profiles take the shape of a separated kink-antikink pair. Classically the soliton energies are invariant under the change of a continuous parameter that can be interpreted as the kink-antikink separation. This is not the case for the VPEs so that quantum effects decide on the energetically most favorable separation. The considered configurations are classically stable so that its quantum fluctuations have only real frequency eigenvalues. Hence, in contrast to the kink-antikink configuration in the ${\varphi }^4$ model, the VPE is well defined for any value of the separation and we gain insight into the quantum corrections to the kink-antikink potential.

• Received 5 December 2022
• Accepted 13 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.036003

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Published by the American Physical Society