Vacuum polarization energy of the Shifman–Voloshin soliton

Abstract

We compute the vacuum polarization energy of soliton configurations in a model with two scalar fields in one space dimension using spectral methods. The second field represents an extension of the conventional φ 4 kink soliton model. We find that the vacuum polarization energy destabilizes the soliton except when the fields have identical masses. In that case the model is equivalent to two independent φ 4 models.

Quantum instabilities of solitons

“…The conclusion on instability has been drawn from numerical results for the VPE in the no-tadpole renormalization scheme. This conclusion remains valid for the physical on-shell scheme [15].…”

“…In Ref. [15] it has been verified that, when a is close to one, the VPE of the Shifman-Voloshin soliton follows closely that of the background potential…”

“…To compute the VPE this requires further extensions of the spectral methods that are described and applied in Refs. [5,15]. Some of the numerical results of that analysis are shown in the right panel of figure 3.…”

Quantum Corrections to Solitons in the $Φ^8$ Model

“…As the kink occupies the secondary vacuum over an increasing region in space, the one-loop quantum energy decreases without a lower bound and thereby destabilizes the kink. This conjecture has been drawn from two model calculations, in the φ 6 model [12,13] and the multi-field Shifman-Voloshin model [14,15]. In the context of the φ 6 model a similar conclusion was drawn when it was observed that fluctuations produce a net force on the kink [16].…”

Quantum Corrections to Soliton Energies

“…By contradiction we thus conclude that 2/µ is an upper bound for χ(0) and we parameterize χ(0) = a 2/µ with 0 ≤ a < 1, for which solitons have been constructed numerically. 50 Observe that φ is in its secondary vacuum at x = 0. The closer a is to unity, the larger the region in which both fields approximately equal their corresponding expectation values from the secondary vacuum.…”