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Scientific paper
Sep 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phdt........10y&link_type=abstract
Thesis (PH.D.)--THE UNIVERSITY OF TEXAS AT AUSTIN, 1986.Source: Dissertation Abstracts International, Volume: 47-05, Section: B,
Other
Zero-Energy Modes, Field Quantization, Cosmic Phase Transitions, Strings
Scientific paper
The Nielsen-Olesen model of strings is generalized to theories with spontaneously broken nonabelian gauge groups. Two new phenomena not possible in the abelian case are pointed out. One is that some of the symmetry generators of the original group may not have a global meaning. This can also happen for the generators of the unbroken subgroup. Another phenomenon is that the entire group of symmetries may not get restored in the core of the vortex. The vortices occurring in a realistic SO(10) Grand Unified Theory (GUT) are discussed in detail. The above mentioned phenomena are exemplified. The Weinberg-Salam symmetry generators are shown to be globally undefinable in some of the vortex sectors. The ansatz for a sector in which a scalar field is nonvanishing in the core of the vortex is constructed. The subgroup of symmetries remaining unbroken in the core is determined. Zero-energy bound states of fermions are known to induce half-integral fermionic charge on solitons. It is argued that such an interpretation of zero-modes is unsatisfactory on physical grounds. An alternative spectrum with integral values of the fermionic charge is constructed. Fermionic zero-modes are found to occur in some of the vortex sectors of the SO(10) GUT model. The induced fermionic charge is computed using the accepted interpretation, and it is found to change from half-integral to integral during the Weinberg-Salam phase transition. It is argued that in this realistic example, an integral spectrum for the fermion number is intuitively more appealing. In the last chapter it is shown that strings could have played the important role of inducing a phase transition in the early universe. Their behaviour is analogous to that of seeds in a supercooled medium. As a result, the phase transition changes from being first order to second order. It is shown that strings that do not have the symmetry group restored in the core are particularly effective in bringing this about. The nucleation of the true vacuum phase on the strings occurs through a real time evolution rather than quantum tunnelling. This is demonstrated with the help of a numerical example. The conditions under which such a phase transition can lead to the observed homogeneous universe are worked out.
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