Vortex condensation in the dual Chern–Simons–Higgs model

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.

Casimir force due to condensed vortices in a plane

“…Vortex condensation in Chern-Simons (CS)-type theories, particularly in selfdual models, have been shown possible for some critical value of the Chern-Simons parameter [14,15], with the determination of the condensation point explicitly obtained in Ref. [13]. The Casimir force for the dual MPCS type of model is studied here in this context, deep inside the vortex condensate phase.…”

“…By properly matching our dual action to a field theory model, it is then possible to write it in terms of a vortex field coupled to a vectorial field (for earlier implementations of this procedure, see, for example, the work done in Refs. [11][12][13], and references therein).…”

“…Following the work in Refs. [12,13], we show that this model can be seen as the dualized version of a Chern-Simons-Higgs (CSH) model, in which the vortex excitations of the CSH model are made explicit and considered in a vacuum state. Vortex condensation in Chern-Simons (CS)-type theories, particularly in selfdual models, have been shown possible for some critical value of the Chern-Simons parameter [14,15], with the determination of the condensation point explicitly obtained in Ref.…”

“…II, we introduce the MPCS model as a particular limit of the vortex model considered in Ref. [13] and summarize the relevant equations and relations that will be of relevance for this work. In Sec.…”

Particle-vortex duality in topological insulators and superconductors

“…This particle-vortex duality has a long history that goes back to the early work on superconductivity of [14,15], and later in the study of anyon superconductivity and the fractional quantum Hall effect in [16] (see also the early work in [17,18]). While the duality can be defined at the level of the path integral [19] and even embedded into the gauge/gravity correspondence [20] (see also [21,22] for another take on a path integral formulation), the formulation that will be most useful for our purposes is the transformation that takes "self-duality in odd dimensions" [23] to a topologically massive theory [24]. This will furnish the necessary tools we need to understand Son's conjectured equivalence between a massless Dirac fermion understood as the boundary mode of a topological insulator, and the composite fermion of an effective low-energy theory for the half-filled Landau level of a Fermi liquid [25], alternatively described in [26,27].…”