Bogomol'nyi vortices from Seiberg-Witten monopoles

Sazzad Mahmud Nasir

doi:10.1142/S0217751X99001822

Bogomol'nyi vortices from Seiberg-Witten monopoles

Sazzad Mahmud Nasir^*

^*Corresponding author for this work

Communication Sciences and Disorders

Research output: Contribution to journal › Article › peer-review

Abstract

The Seiberg-Witten monopole equations are studied on manifolds of type X = Σ × S², where Σ is a Riemann surface of genus g > 1. Imposing spherical symmetry on the monopole equations, Bogomol'nyi vortices on Σ are obtained. The dimensions of the two moduli spaces agree. As a consistency check, we show that all solutions to the monopole equations on X that descend to Σ are spherically symmetric. Further, Bogomol'nyi vortices on S² are obtained as dimensional reduction of the monopole equations on S². Finally, the Seiberg-Witten "invariant" in these cases are briefly discussed.

Original language	English (US)
Pages (from-to)	3905-3920
Number of pages	16
Journal	International Journal of Modern Physics A
Volume	14
Issue number	24
DOIs	https://doi.org/10.1142/S0217751X99001822
State	Published - Sep 30 1999

Funding

I am very much indebted to Professor N. S. Manton for suggesting this problem to me and for discussions that I have had with him during the course of this work. I would also like to thank Dr. C. Houghton and Dr. H. Merabet for helpful comments on this manuscript. This work was supported by the Overseas Research Scheme, the Cambridge Commonwealth Trust and Wolfson college.

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Nuclear and High Energy Physics
Astronomy and Astrophysics

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10.1142/S0217751X99001822

Cite this

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title = "Bogomol'nyi vortices from Seiberg-Witten monopoles",

abstract = "The Seiberg-Witten monopole equations are studied on manifolds of type X = Σ × S2, where Σ is a Riemann surface of genus g > 1. Imposing spherical symmetry on the monopole equations, Bogomol'nyi vortices on Σ are obtained. The dimensions of the two moduli spaces agree. As a consistency check, we show that all solutions to the monopole equations on X that descend to Σ are spherically symmetric. Further, Bogomol'nyi vortices on S2 are obtained as dimensional reduction of the monopole equations on S2. Finally, the Seiberg-Witten {"}invariant{"} in these cases are briefly discussed.",

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N2 - The Seiberg-Witten monopole equations are studied on manifolds of type X = Σ × S2, where Σ is a Riemann surface of genus g > 1. Imposing spherical symmetry on the monopole equations, Bogomol'nyi vortices on Σ are obtained. The dimensions of the two moduli spaces agree. As a consistency check, we show that all solutions to the monopole equations on X that descend to Σ are spherically symmetric. Further, Bogomol'nyi vortices on S2 are obtained as dimensional reduction of the monopole equations on S2. Finally, the Seiberg-Witten "invariant" in these cases are briefly discussed.

AB - The Seiberg-Witten monopole equations are studied on manifolds of type X = Σ × S2, where Σ is a Riemann surface of genus g > 1. Imposing spherical symmetry on the monopole equations, Bogomol'nyi vortices on Σ are obtained. The dimensions of the two moduli spaces agree. As a consistency check, we show that all solutions to the monopole equations on X that descend to Σ are spherically symmetric. Further, Bogomol'nyi vortices on S2 are obtained as dimensional reduction of the monopole equations on S2. Finally, the Seiberg-Witten "invariant" in these cases are briefly discussed.

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Bogomol'nyi vortices from Seiberg-Witten monopoles

Abstract

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ASJC Scopus subject areas

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