Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry

We discuss the homological aspects of the connection between quantum string generating function and the formal power series associated to the dimensions of chains and homologies of suitable Lie algebras. Our analysis can be considered as a new straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of $SL(2,{\mathbb Z})$) to the partition functions of Lagrangian branes, refined vertex and open string partition functions, represented by means of formal power series that encode Lie algebra properties. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras and in the role of Selberg-type spectral functions of an hyperbolic three-geometry associated with $q$-series in the computation of the string amplitudes.Comment: Revised version. References added, results remain unchanged. arXiv admin note: text overlap with arXiv:hep-th/0701156, arXiv:1105.4571, arXiv:1206.0664 by other author

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

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

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

Dynamic RKKY interaction in graphene

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, based on which the energetically favourable alignment between magnetic moments embedded in this material can be calculated. The general consensus is that the strength of the RKKY interaction in graphene decays as 1/D3 or faster, where D is the separation between magnetic moments. Such an unusually fast decay for a 2-dimensional system suggests that the RKKY interaction may be too short ranged to be experimentally observed in graphene. Here we show in a mathematically transparent form that a far more long ranged interaction arises when the magnetic moments are taken out of their equilibrium positions and set in motion. We not only show that this dynamic version of the RKKY interaction in graphene decays far more slowly but also propose how it can be observed with currently available experimental methods.Comment: 7 pages, 2 figures, submitte

Scalar and Spinor Particles in the Spacetime of a Domain Wall in String Theory

We consider scalar and spinor particles in the spacetime of a domain wall in the context of low energy effective string theories, such as the generalized scalar-tensor gravity theories. This class of theories allows for an arbitrary coupling of the wall and the (gravitational) scalar field. First, we derive the metric of a wall in the weak-field approximation and we show that it depends on the wall's surface energy density and on two post-Newtonian parameters. Then, we solve the Klein-Gordon and the Dirac equations in this spacetime. We obtain the spectrum of energy eigenvalues and the current density in the scalar and spinor cases, respectively. We show that these quantities, except in the case of the energy spectrum for a massless spinor particle, depend on the parameters that characterize the scalar-tensor domain wall.Comment: LATEX file, 21 pages, revised version to appear in Phys. Rev.