# Topologically Massive Abelian Gauge Theory

Source: [Topologically Massive Abelian Gauge Theory](<https://www.sota2.com/research/paper/68fa23222c2a37601939308b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:23.732Z

Authors: K. Saygili

Published: 2007-11-25T10:38:12.000Z

## Abstract

We discuss three mathematical structures which arise in topologically massive abelian gauge theory. First, the euclidean topologically massive abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the euclidean theory in cartesian coordinates on R3 which are given by (anti-)holomorpic functions. The orthogonality relation of contact structures which are determined by the real parts of these complex solutions separates them into two classes: the self-dual and the anti-self-dual solutions. Thirdly, we apply the curl transformation to this theory. An arbitrary solution is given by a vector tangent to a sphere whose radius is determined by the topological mass in transform space. Meanwhile a gauge transformation corresponds to a vector normal to this sphere. We discuss the quantization of topological mass on an example.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0711.3893>)

[PDF](<https://arxiv.org/pdf/0711.3893.pdf>)