We have examined vortex solutions in (2+ l)D Chem-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 the corresponding general n-vortex solutions should contain 2n free parameters.Various characteristics of Chem-Simons vortices are discussed briefly.PACS numbers: 11.15. -q, 11.17.+y, 74.65.+n During the last two decades the study of vortices has become an interdisciplinary subject between condensedmatter physics and particle physics. Ginzburg-Landau theory, the macroscopic theory of superconductivity, was known to admit localized solutions of the vortex type. ' So does the Abelian Higgs model, which is the relativistic extension of the Ginzburg-Landau theory. Characteristically, these vortex solutions carry magnetic flux but are electrically neutral.Understanding the physics of the recently discovered high-T, superconductors is one of the most important problems at the moment. As emphasized by several authors, this new superconductor is characterized by its two-dimensional nature, and a P-and T-violating statistical interaction might be important in describing this system. In field-theory language, this P-and T-violating interaction can be related to the Chem-Simons term in (2+1)D Abelian gauge theory, which had been studied by various theorists in other contexts. The basic object in this model behaves like anyons, flux-tube-chargedparticle composites with unusual statistics. One usually takes the vortex solution in the Ginzburg-Landau theory as this flux tube. But there is another possibility. With the introduction of the Chem-Simons term in the Abelian Higgs model, it was observed that there also exist vortex solutions. These Chem-Simons vortices are different from the Nielsen-Olesen vortices in that they carry electric charge as well as magnetic flux. Therefore, it is worthwhile to consider the Chem-Simons vortices as another candidate for anyonlike objects. The solutions studied by the authors of Refs. 4 and 5 are, however, very complicated and therefore it is difficult to check many interesting properties with them. This complication arises from the existence of the Maxwell term, aside from the Chem-Simons term, in the action. Here we would like to point out that to have Chem-Simons vortices, the Maxwell term is not a necessity. It is not unreasonable to consider the theory without the Maxwell term because the Chem-Simons term is dominant over the Maxwell term in the longdistance region (or, equivalently, in the limit of large tt, the coefficient of the Chem-Simons term). Moreover, very recently, Deser and Yang observed that the Higgs 4 eg 2 I l I FIG. 1. The shape of the scalar potential for the NielsenOlesen-type vortices in the Bogomol'nyi limit.mechanism can transmute a nondynamical gauge field into a massive gauge boson. Therefore the dynamics is not lost even in the absence of the Maxwell term provided that there is a Higgs mechanism. As we will show in this paper, the Chem-Simons-Higgs theo...

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