Vortices in vacuumless systems (Q2414999)

Summary: 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.