Abstract
We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first-order formalism that helps us to find the solutions and their respective electromagnetic fields and energy densities. As a bonus, we get to calculate the energy without knowing the explicit solutions. Even though the solutions present a large “tail” which goes far away from the origin, the magnetic flux remains a well defined topological invariant.
Highlights
In high energy physics, topological structures appear in a diversity of contexts and have been vastly studied over the years [1, 2]
We deal with an action in (2, 1) flat spacetime dimensions for a complex scalar field and a gauge field governed by the Maxwell dynamics
We have investigated vortices in vacuumless systems with Maxwell and Chern-Simons dynamics
Summary
Topological structures appear in a diversity of contexts and have been vastly studied over the years [1, 2]. The first relativistic model that supports these objetcs was studied in [19, 20], with the action of a complex scalar field coupled to a gauge field under the symmetry U(1) in Maxwell dynamics These structures are electrically neutral and engender a quantized flux which is conserved and works as a topological invariant. One can investigate these structures with the dynamics of the gauge field governed by the ChernSimons term [23,24,25] In this case, the vortex presents a quantized flux, which is topological invariant, and a Advances in High Energy Physics quantized electric charge.
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