We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed ChernSimons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the chargevortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called

Using quenched chiral perturbation theory we compute meson correlation functions at finite volume and fixed gauge field topology. We also present the corresponding analytical predictions for the unquenched theory at fixed gauge field topology. These results can be used to measure the low-energy parameters of the chiral Langrangian from lattice simulations in volumes much smaller than one pion Compton wavelength.

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivty is concretely realized as global superconductivty in Josephson junction arrays. PACS numbers:The discovery of the fractional quantum Hall [1] effect has revealed the existence of a new state of matter characterized by a new type of order: topological order [2]. Topological order is a particular type of quantum order describing zero-temperature properties of a ground state with a gap for all excitations. Its hallmark are the degeneracy of the ground state on manifolds with non-trivial topology, and excitations with fractional spin and statistics, called anyons [3]. The longdistance properties of these topological fluids are described by Chern-Simons field theories [4] with compact gauge group, which break P-and T-invariance. Other examples of P-and T-breaking topological fluids are given by chiral spin liquids [5].After Laughlin's discovery of topological quantum fluids, it was conjectured that a similar mechanism, based on anyon condensation, could be at the origin of high-T c superconductivity [3]. Unfortunately, there is no evidence of the associated broken P-and T-invariance in the high-T c materials.Here we propose a superconductivity mechanism which is based on a topologically ordered ground state rather than on the usual Landau mechanism of spontaneous symmetry breaking.Contrary to anyon superconductivity it works in any dimension and it preserves P-and T-invariance. In particular we will discuss the lowenergy effective field theory, what would be the Landau-Ginzburg formulation for conventional superconductors.Topologically ordered superconductors have a longdistance hydrodynamic action which can be entirely formulated in terms of generalized compact gauge fields, the dominant term being the topological BF action.BF theories are topological theories that can be defined on manifolds M d+1 of any dimension (here d is the number of spatial dimensions) and play a crucial role in * Electronic address: cristina.diamantini@pg.infn.it † Electronic address: pasquale.sodano@pg.infn.it ‡ Electronic address: ca.trugenberger@InfoCodex.com models of two-dimensional gravity [6]. In [7] we have shown that the BF term also plays a crucial role in the physics of Josephson junction arrays. The BF term [8] is the wedge product of a p-form B and the curvature dA of a (d-p) form A:where k is a dimensionless coupling constant. This can also be written asThe integration by parts does not imply any surface term since we will concentrate on compact spatial manifolds without boundaries and we require that the fields go to pure gauge configuration at infinity in the time direction. Indeed thi...

One of the most profound aspects of the standard model of particle physics, the mechanism of confinement binding quarks into hadrons, is not sufficiently understood. The only known semiclassical mechanism of confinement, mediated by chromo-electric strings in a condensate of magnetic monopoles still lacks experimental evidence. Here we show that the infinite resistance superinsulating state, which emerges on the insulating side of the superconductor-insulator transition in superconducting films offers a realization of confinement that allows for a direct experimental access. We find that superinsulators realize a single-color version of quantum chromodynamics and establish the mapping of quarks onto Cooper pairs. We reveal that the mechanism of superinsulation is the linear binding of Cooper pairs into neutral "mesons" by electric strings. Our findings offer a powerful laboratory for exploring and testing the fundamental implications of confinement, asymptotic freedom, and related quantum chromodynamics phenomena via the desktop experiments on superconductors.

We consider several aspects of 'confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to the Polyakov action in the semiclassical approximation. In 4D we introduce a 'θ-term' and compute the low-energy effective action for the confining string in a derivative expansion. We find that the coefficient of the extrinsic curvature (stiffness) is negative, confirming previous proposals. In the absence of a θ-term, the effective string action is only a cut-off theory for finite values of the coupling e, whereas for generic values of θ, the action can be renormalized and to leading order we obtain the Nambu-Goto action plus a topological 'spin' term that could stabilize the system.