Gauge theories of Josephson junction arrays

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 Chern-Simons 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 charge-vortex 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 BF system, with an antisymmetric Kalb-Ramond gauge field.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 Chern-Simons 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 charge-vortex 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 BF system, with an antisymmetric Kalb-Ramond gauge field.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 a periodic mixed Chern-Simons 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 charge-vortex 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 BF system with an antisymmetric Kalb-Ramond gauge field

Confining Strings at High Temperature

We show that the high-temperature behaviour of the recently proposed confining strings reproduces exactly the correct large-N QCD result, for a large class of truncations of the long-range interaction between surface elements.Comment: 8 pages, no figure

SU(N) Antiferromagnets and Strongly Coupled QED: Effective Field Theory for Josephson Junctions Arrays

We review our analysis of the strong coupling of compact QED on a lattice with staggered Fermions. We show that, for infinite coupling, compact QED is exactly mapped in a quantum antiferromagnet. We discuss some aspects of this correspondence relevant for effective field theories of Josephson junctions arrays.Comment: 33 pages,latex,Proceedings of "Common Trends in Condensed Matter and High Energy Physics",DFUPG 1/9

Topological Defects in Gauge Theories of Open p-branes

We study phase transitions induced by topological defects in Abelian gauge theories of open p-branes in (d+1) space-time dimensions. Starting from a massive antisymmetric tensor theory for open p-branes we show how the condensation of topological defects can lead to a decoupled phase with a massless tensor coupled to closed (p-1)-branes and a massive tensor coupled to open (p+1)-branes. We also consider the case, relevant in string theory, in which the boundaries of the p-branes are constrained to live on a Dirichlet n-branes.Comment: 16 pages, harvmac te

Quantum effects of a massive 3-form coupled to a Dirac field

We consider the coupling of A_{\mu\nu\rho} to the generic current of matter field, later identified with the spin density current of a Dirac field. In fact, one of the objectives of this paper is to investigate the impact of the quantum fluctuations of A_{\mu\nu\rho} on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for A_{\mu\nu\rho}. In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of A_{\mu\nu\rho} and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, A_{\mu\nu\rho} contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of A_{\mu\nu\rho} since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of A_{\mu\nu\rho} already expected from the earlier calculation of the Wilson loop.Comment: 10 pages, Revtex, no figures; in print on Phys.Rev.D; added new reference

Finite-volume meson propagators in quenched chiral perturbation theory

We compute meson propagators in finite-volume quenched chiral perturbation theory.Comment: 3 pages, Lattice2001(chiral fermions

SU(N) Quantum Antiferromagnets and the Phase Structure of QED in the Strong Coupling Limit

We examine the strong coupling limit of both compact and non compact QED on a lattice with staggered fermions. We show that every SU(N) antiferromagnet with spins in a particular fundamental representation of the SU(N) Lie Algebra and with nearest neighbor couplings on a bipartite lattice is exactly equivalent to the infinite coupling limit of lattice QED with the numbers of flavors of electrons related to N and the dimension of spacetime D+1. We find that,for both compact and noncompact QED,when N is odd the ground state of the strong coupling limit breaks chiral symmetry in any dimensions and for any N and the condensate is an isoscalar mass operator. When N is even,chiral symmetry is broken if D is bigger or equal to 2 and N is small enough and the order parameter is an isovector mass operator. We also find the exact ground state of the lattice Coulomb gas as well as a variety of related lattice statistical systems with long ranged interactions.Comment: latex, 45 pages, DFUPG 69/9

Self Duality and Oblique Confinement in Planar Gauge Theories

We investigate the non-perturbative structure of two planar $Z_p \times Z_p$ lattice gauge models and discuss their relevance to two-dimensional condensed matter systems and Josephson junction arrays. Both models involve two compact U(1) gauge fields with Chern-Simons interactions, which break the symmetry down to $Z_p \times Z_p$. By identifying the relevant topological excitations (instantons) and their interactions we determine the phase structure of the models. Our results match observed quantum phase transitions in Josephson junction arrays and suggest also the possibility of {\it oblique confining ground states} corresponding to quantum Hall regimes for either charges or vortices.Comment: 32 pages, harvma

Chiral Dynamics and Fermion Mass Generation in Three Dimensional Gauge Theory

We examine the possibility of fermion mass generation in 2+1- dimensional gauge theory from the current algebra point of view.In our approach the critical behavior is governed by the fluctuations of pions which are the Goldstone bosons for chiral symmetry breaking. Our analysis supports the existence of an upper critical number of Fermion flavors and exhibits the explicit form of the gap equation as well as the form of the critical exponent for the inverse correlation lenght of the order parameterComment: Latex,10 pages,DFUPG 70/9

Phase Transitions and Mass Generation in 2+1 Dimensions

The possibility that the epsilon expansion can predict the order of phase transitions in three dimensional field theories is examined. For a Hermitean matrix-valued order parameter, the epsilon expansion predicts fluctuation induced first order phase transitions. We analyze two 2+1-dimensional quantum field theories which exhibit spontaneous symmetry breaking and have martix order parameters. Using the large $N$ expansion, we show that these models exhibit second order transitions and discuss the implications for the chiral symmetry breaking transition in 2+1-dimensional QCD for a critical number of quark flavors.Comment: published in Phys. Rev. D50, 1060 (1994