Topologically massive magnetic monopoles

Classical and Quantum Gravity (Impact Factor: 3.1). 05/2000; DOI: 10.1088/0264-9381/17/19/310
Source: arXiv

ABSTRACT We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution.

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    ABSTRACT: We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space by means of an SU(1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge transformation. Then we present map including the topological mass which is the Lorentzian analog of the Hopf map. This map yields a global decomposition of as a trivial bundle over the upper portion of the pseudosphere which is the Hyperboloid model for the Lobachevski geometry. This leads to a reduction of the Abelian field equation onto using a global section of the solution on . Then we discuss the integration of the field equation using the Archimedes map . We also present a brief discussion of the holonomy of the gauge potential and the dual field strength on .
    International Journal of Modern Physics A 01/2012; 22(16n17). · 1.09 Impact Factor
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    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 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 in an example.
    International Journal of Modern Physics A 01/2012; 23(13). · 1.09 Impact Factor
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    ABSTRACT: The bibliography compilation on magnetic monopoles is updated to include references from 2000 till mid 2011. It is intended to contain all experimental papers on the subject and only the theoretical papers which have specific experimental implications.


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