Dual approaches for defects condensation

We review two methods used to approach the condensation of defects phenomenon. Analyzing in details their structure, we show that in the limit where the defects proliferate until occupy the whole space these two methods are dual equivalent prescriptions to obtain an effective theory for the phase where the defects (like monopoles or vortices) are completely condensed, starting from the fundamental theory defined in the normal phase where the defects are diluted.Comment: 7 pages, major modifications. Version accepted for publication in Physics Letters

Massive photons and Dirac monopoles: electric condensate and magnetic confinement

We use the generalized Julia-Toulouse approach (GJTA) for condensation of topological currents (charges or defects) to argue that massive photons can coexist consistently with Dirac monopoles. The Proca theory is obtained here via GJTA as a low energy effective theory describing an electric condensate and the mass of the vector boson is responsible for generating a Meissner effect which confines the magnetic defects in monopole-antimonopole pairs connected by physical open magnetic vortices described by Dirac brane invariants, instead of Dirac strings.Comment: 6 pages, version accepted for publication in Physics Letters

Accessing the topological susceptibility via the Gribov horizon

The topological susceptibility, $\chi^4$, following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the $\eta^{\prime}$ mass, the so-called $U(1)_{A}$ problem. A nonzero $\chi^4$ is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current. In a recent paper (Phys.Rev.Lett.114 (2015) 24, 242001), an explicit relationship between this Veneziano ghost and color confinement was proposed, by connecting the dynamics of the Veneziano ghost, and thus the topological susceptibility, with Gribov copies. However, the analysis is incompatible with BRST symmetry (Phys.Rev.D 93 (2016) no.8, 085010). In this paper, we investigate the topological susceptibility, $\chi^4$, in SU(3) and SU(2) Euclidean Yang-Mills theory using an appropriate Pad\'e approximation tool and a non-perturbative gluon propagator, within a BRST invariant framework and by taking into account Gribov copies in a general linear covariant gauge.Comment: 17 pages, 4 figures. v2: corrected typos, new figures, improved style of presentatio

On the duality in four-dimensional Lorentz-breaking field theories

We consider new issues of duality in four-dimensional Lorentz-breaking field theories. In particular, we demonstrate that the arising of the aether-like Lorentz-breaking term is necessary in order for the 4D models to display the duality analog between the MCS and self-dual models in 3D. We further study the dispersion relations in both theories and discuss the physical contents of the models involved in this new dualilty.Comment: 16 page