Phase transition in the Higgs model of scalar dyons

In the present paper we investigate the phase transition "Coulomb--confinement" in the Higgs model of abelian scalar dyons -- particles having both, electric $e$ and magnetic $g$, charges. It is shown that by dual symmetry this theory is equivalent to scalar fields with the effective squared electric charge e^{*2}=e^2+g^2. But the Dirac relation distinguishes the electric and magnetic charges of dyons. The following phase transition couplings are obtained in the one--loop approximation: \alpha_{crit}=e^2_{crit}/4\pi\approx 0.19, \tilde\alpha_{crit}=g^2_{crit}/4\pi\approx 1.29 and \alpha^*_{crit}\approx 1.48.Comment: 16 pages, 2 figure

Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid Vacau

The role in string theory of manifolds of complex dimension $D_{crit} + 2(Q-1)$ and positive first Chern class is described. In order to be useful for string theory, the first Chern class of these spaces has to satisfy a certain relation. Because of this condition the cohomology groups of such manifolds show a specific structure. A group that is particularly important is described by $(D_{crit} + Q-1, Q-1)$--forms because it is this group which contains the higher dimensional counterpart of the holomorphic $(D_{crit}, 0)$--form that figures so prominently in Calabi--Yau manifolds. It is shown that the higher dimensional manifolds do not, in general, have a unique counterpart of this holomorphic form of rank $D_{crit}$. It is also shown that these manifolds lead, in general, to a number of additional modes beyond the standard Calabi--Yau spectrum. This suggests that not only the dilaton but also the other massless string modes, such as the antisymmetric torsion field, might be relevant for a possible stringy interpretation.Comment: 7 pages, NSF-ITP-93-3

Pseudo-Stable Bubbles

The evolution of spherically symmetric unstable scalar field configurations (``bubbles'') is examined for both symmetric (SDWP) and asymmetric (ADWP) double-well potentials. Bubbles with initial static energies E_0\la E_{{\rm crit}}, where $E_{{\rm crit}}$ is some critical value, shrink in a time scale determined by their linear dimension, or ``radius''. Bubbles with E_0\ga E_{{\rm crit}} evolve into time-dependent, localized configurations which are {\it very} long-lived compared to characteristic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.tic time-scales in the models examined. The stability of these configurations is investigated and possible applications are briefly discussed.Comment: 10 pages, LaTeX (uses revtex 3.0), 4 figures (postscript files of figs.1 and 2 appended starting on line 497), report DART-HEP-93/0