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Register a new userQuantum Corrections to Solitons in the $Phi^8$ Model
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We compute the vacuum polarization energy of kink solitons in the $phi^{8}$ model in one space and one time dimensions. There are three possible field potentials that have eight powers of $phi$ and that possess kink solitons. For these different field potentials we investigate whether the vacuum polarization destabilizes thesolitons. This may particularly be the case for those potentials that have degenerate ground states with different curvatures in field space yielding different thresholds for the quantum fluctuations about the solitons at negative and positive spatial infinity. We find that destabilization occurs in some cases, but this is not purely a matter of the field potential but also depends on the realized soliton solution for that potential. One of the possible field potentials has solitons with different topological charges. In that case the classical mass approximately scales like the topological charge. Even though destabilization precludes robust statements, there are indications that the vacuum polarization energy does not scale as the topological charge.
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We review some recent developments in the subject of quantum corrections to soliton mass and central charge. We consider in particular approaches which use local densities for these corrections, as first discussed by Hidenaga Yamagishi. We then consider dimensional regularization of the supersymmetric kink in 1+1 dimensions and an extension of this method to a 2+1-dimensional gauge theory with supersymmetric abelian Higgs vortices as the solitons.
The Nicole model is a conformal field theory in three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to numerically construct soliton solutions for all Hopf charges from one to eight. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than two and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.
The Aratyn-Ferreira-Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which have been found analytically. Axial, knot and linked solitons are found numerically to be static solutions using a modified volume preserving flow for Hopf index one to eight, allowing for comparison with other Hopf soliton models. Solutions include a static trefoil knot at Hopf index five. A one-parameter family of conformal Skyrme-Faddeev (CSF) models, consisting of linear combinations of the Nicole and AFZ models, are also investigated numerically. The transition of solutions for Hopf index four is mapped across these models. A topological change between linked and axial solutions occurs, with fewer models permitting axial solitons than linked solitons at Hopf index four.
A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU(2), and local (gauge), U(1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is of 90 degrees. The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.
We study boundary scattering in the $phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to include regimes of near-elastic scattering, the restoration of a missing scattering window, and the creation of a kink or oscillon through the collision-induced decay of a metastable boundary state. We also study the decay of the vibrational boundary mode, and explore different scenarios for its relaxation and for the creation of kinks.
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