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2015•Durham e-Theses (Durham University)Open access

A Study of Noncommutative Instantons

Andrew Iskauskas

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Abstract

We consider the properties and behaviour of 2 U(2) noncommutative instantons: solutions of the NC-deformed ADHM equations which arise from U(2) 5d Yang-Mills \ntheory. The ADHM construction allows us to find all such solutions, which form a moduli space of allowed configurations. We derive the metric for such a space, and consider the dynamics of the instantons on this space using the Manton approximation. We examine the reduction of this system to lower-dimensional soliton theories, and finally consider the effect of adding a Higgs field to the SYM theory, resulting in a potential on the instanton moduli space.

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We consider the properties and behaviour of 2 U(2) noncommutative instantons: solutions of the NC-deformed ADHM equations which arise from U(2) 5d Yang-Mills \ntheory. The ADHM construction allows us to find all such solutions, which form a moduli space of allowed configurations. We derive the metric for such a space, and consider the dynamics of the instantons on this space using the Manton approximation. We examine the reduction of this system to lower-dimensional soliton theories, and finally consider the effect of adding a Higgs field to the SYM theory, resulting in a potential on the instanton moduli space.

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Available abstract

We consider the properties and behaviour of 2 U(2) noncommutative instantons: solutions of the NC-deformed ADHM equations which arise from U(2) 5d Yang-Mills \ntheory. The ADHM construction allows us to find all such solutions, which form a moduli space of allowed configurations. We derive the metric for such a space, and consider the dynamics of the instantons on this space using the Manton approximation. We examine the reduction of this system to lower-dimensional soliton theories, and finally consider the effect of adding a Higgs field to the SYM theory, resulting in a potential on the instanton moduli space.

Key concepts: Instanton, Noncommutative geometry, Moduli space, Metric (unit), Space (punctuation), Higgs boson, Noncommutative quantum field theory, Mathematical physics

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