Remarks on a compact Abelian Higgs model

Abstract

Aspects of screening and confinement are re-examined for a recently proposed compact Abelian Higgs model with a θ-term. Our discussion is accomplished using the gauge-invariant but pathdependent variables formalism, which is an alternative to the Wilson loop approach. We explicitly show that the static potential profile is the sum of an effective-Yukawa and a linear potential, leading to the confinement of static external charges. We point out the central rôle of the parameter measuring the stiffness of the vortex lines present in the model in both the Yukawa-like and the confining sectors of the effective inter-particle potential we have computed. 12.60.Cn, 13.40.Gp Condensed matter physics and quantum field theory have, in the last few years, become increasingly closely meshed [1,2]. The physical consequences of this new physics have triggered a large body of literature. An interesting and illustrative example on this subject arises when one considers topological insulators and topological superconductors, where topological insulators have been experimentally realized in various materials. Incidentally, it is worth noting that these states are characterized by topological properties rather than usual properties such as symmetries preserved (or broken) by some order parameter. At the same time, it may be recalled that the θ-term (or axion-term) has been the key ingredient of these developments, which produces non-trivial effects such as the Witten effect [3-5] and topological magneto-electric effect [6,7].As already expressed, the precedent states are described by a low-energy field theory which is a topological field theory. For instance, recently a topological field theory description of (1 + 3)-D topological superconductors has been discussed [8]. In this work, the topological superconductor is described through a topological coupling between the electromagnetic field and the superconducting phase fluctuation, in much the same way as the coupling of axions with an Abelian gauge field.Most recently, it has been shown that a compact Abelian Higgs model with a θ-term in (1 + 3)-D may be considered as an effective field theory for a topological Mott insulator [9]. Interestingly, it was also shown that this effective theory is dual to an axionic superconductor model [3], which contains both particle and vortex degrees of freedom. Curiously, it should be noted that this dual theory is analogous to a superconducting vortex strings [10]. Mention should be made, at this point, to an equivalent condensed matter picture from the above studies, where the vortex lines play the role of magnetic * Electronic address: patricio.gaete@usm.cl † Electronic address: helayel@cbpf.br monopoles [9]. Let us also mention here that, in the case without matter, the previous compact Higgs model becomes a compact electrodynamics with a theta term, which is confining. It should be recalled that the existence of a phase structure for the continuum Abelian U(1) gauge theory was first obtained by including the effects due to the compactne...