Abstract
The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern–Simons–Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern–Simons–Higgs model, we determine the location of the critical value for the Chern–Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.
Highlights
Gauge field theories in two spatial dimensions have long been recognized as important for understanding several physical phenomena that can be well approximated as planar ones, like high temperature superconductors and the fractional quantum Hall effect
Another important aspect regarding CS gauge theories, when coupled to symmetry broken scalar potentials, is the existence of both topological and nontopological vortex solutions [3]. These vortices are charged and anyon-like solutions that may be of relevance in explaining several phenomena in planar condensed matter systems, like in high temperature superconductors and the fractional quantum Hall effect, already mentioned above
By restricting the study of the obtained dual action in the London limit for the scalar Higgs field, ρ = ρ0 ≡ ρ taken as constant and considering the classical self-dual vortex solutions, the vortex degrees of freedom in the partition function action can be matched to a field theory model in terms of a vortex field with a dynamical mass for the vortices
Summary
Gauge field theories in two spatial dimensions have long been recognized as important for understanding several physical phenomena that can be well approximated as planar ones, like high temperature superconductors and the fractional quantum Hall effect. Another important aspect regarding CS gauge theories, when coupled to symmetry broken scalar potentials, is the existence of both topological and nontopological vortex solutions [3] These vortices are charged and anyon-like solutions that may be of relevance in explaining several phenomena in planar condensed matter systems, like in high temperature superconductors and the fractional quantum Hall effect, already mentioned above. In this work we consider the vortex condensation in the CSH model specialized to the case of the self-dual potential for the scalar field [4, 5], in which case vortices can be considered as noninteracting This is used only for convenience, since explicit expressions for the vortex energy and the dynamical mass for the vortices follow.
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