Various aspects of duality in a series of Abelian lattice models defined on topologically
non-trivial lattices are investigated. The dual theories on non-trivial spaces are found
to contain extra topological degrees of freedom in addition to the usual local ones. By
exploiting this fact, it is possible to introduce topological modes in the defining partition
function such that the dual model contains a reduced set of topological degrees of freedom.
Such a mechanism leads to the possibility of constructing self-dual lattice models
even when the naive theory fails to be self-dual. After writing the model in field-strength
formalism the topological modes are identified as being responsible for the quantization
of global charges. Using duality, correlators in particular dimensions are explicitly constructed,
and the topological modes are shown to lead to inequivalent sectors of the theory
much like the inequivalent ^-sectors in non-Abelian gauge theories. Furthermore, duality
is applied to the study of finite-temperature compact U(l), and previously unknown
source terms, which arise in the dual Coulomb gas representation and consequently in the
associated Sine-Gordon model, are identified. Finally, the topological modes are demonstrated
to be responsible for the maintenance of target-space duality in lattice regulated
bosonic string theory and automatically lead to the suppression of vortex configurations
which would otherwise destroy the duality. / Science, Faculty of / Physics and Astronomy, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/9998 |
| Date | 11 1900 |
| Creators | Jaimungal, Sebastian |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Format | 7540635 bytes, application/pdf |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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