×

Multivortex solutions of the abelian Chern-Simons-Higgs theory. (English) Zbl 1014.58500

Summary: We have examined vortex solutions in \((2+1)\)D Chern-Simons-Higgs theory which has no usual Maxwell term. It is shown that the Bogomol’nyi-type equations can be derived for a simple sixth-order Higgs potential and corresponding general \(n\)-vortex solutions should contain \(2n\) free parameters. Various characteristics of Chern-Simons vortices are discussed briefly.

MSC:

58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
35Q60 PDEs in connection with optics and electromagnetic theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
81T13 Yang-Mills and other gauge theories in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] V. L. Ginzburg, Zh. Eksp. Teor. Fiz. 20 pp 1064– (1950)
[2] A. A. Abrikosov, Sov. Phys. JETP 5 pp 1174– (1957)
[3] H. B. Nielsen, Nucl. Phys. B61 pp 45– (1973) · doi:10.1016/0550-3213(73)90350-7
[4] F. Wilczek, Phys. Rev. Lett. 49 pp 957– (1982) · doi:10.1103/PhysRevLett.49.957
[5] S. K. Paul, Phys. Lett. B 174 pp 420– (1986) · doi:10.1016/0370-2693(86)91028-2
[6] H. J. de Vega, Phys. Rev. Lett. 56 pp 2564– (1986) · doi:10.1103/PhysRevLett.56.2564
[7] C. N. Kumar, Phys. Lett. B 178 pp 395– (1986) · doi:10.1016/0370-2693(86)91400-0
[8] S. Deser, Mod. Phys. Lett. A 4 pp 2123– (1989) · doi:10.1142/S0217732389002380
[9] S. Deser, Phys. Lett. 139B pp 371– (1984) · doi:10.1016/0370-2693(84)91833-1
[10] E. B. Bogomol’nyi, Sov. J. Nucl. Phys. 24 pp 449– (1976)
[11] E. J. Weinberg, Phys. Rev. D 19 pp 3008– (1979) · doi:10.1103/PhysRevD.19.3008
[12] L. Jacobs, Phys. Rev. B 19 pp 4486– (1979) · doi:10.1103/PhysRevB.19.4486
[13] C. H. Taubes, Commun. Math. Phys. 72 pp 277– (1980) · Zbl 0451.35101 · doi:10.1007/BF01197552
[14] C. H. Taubes, Commun. Math. Phys. 75 pp 207– (1980) · Zbl 0448.58029 · doi:10.1007/BF01212709
[15] A. N. Redlich, Phys. Rev. Lett. 52 pp 18– (1984) · doi:10.1103/PhysRevLett.52.18
[16] A. N. Redlich, Phys. Rev. D 29 pp 2366– (1984) · doi:10.1103/PhysRevD.29.2366
[17] R. Jackiw, Phys. Rev. Lett. 64 pp 2234– (1990) · Zbl 1050.81595 · doi:10.1103/PhysRevLett.64.2234
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.