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Dualities in Abelian statistical models Jaimungal, Sebastian

Abstract

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.

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