Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page

XY models with disorder and symmetry-breaking fields in two dimensions

The combined effect of disorder and symmetry-breaking fields on the two-dimensional XY model is examined. The study includes disorder in the interaction among spins in the form of random phase shifts as well as disorder in the local orientation of the field. The phase diagrams are determined and the properties of the various phases and phase transitions are calculated. We use a renormalization group approach in the Coulomb gas representation of the model. Our results differ from those obtained for special cases in previous works. In particular, we find a changed topology of the phase diagram that is composed of phases with long-range order, quasi-long-range order, and short-range order. The discrepancies can be ascribed to a breakdown of the fugacity expansion in the Coulomb gas representation. Implications for physical systems such as planar Josephson junctions and the faceting of crystal surfaces are discussed.Comment: 17 pages Latex with 5 eps figures, change: acknowledgment extende

Complex flow patterns at the onset of annular electroconvection in a dielectric liquid subjected to an arbitrary unipolar injection

We numerically investigated the annular electroconvection that takes place in a dielectric liquid lying between two concentric cylinder electrodes. A uniform injection of arbitrary strengths either from the inner or outer cylinder introduces free charge carriers into the system, and the resulting Coulomb force induces electroconvection. The problem is characterized by a linear instability that corresponds to the onset of flow motion. The linear stability criteria were determined from direct numerical results and by linear stability analysis, and the results obtained with the two approaches show an excellent agreement. We focused on the fully developed flow pattern in the finite amplitude regime. We observed very different flow motions that were highly dependent on the injection strength.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Cross-Border Trade: A Two-Stage Equilibrium Model of the Florence Regulatory Forum Proposals

Cross-Border Trade: A Two-Stage Equilibrium Model of the Florence Regulatory Forum Proposal

Electro-osmotic flow in coated nanocapillaries: a theoretical investigation

Motivated by recent experiments, we present a theoretical investigation of how the electro-osmotic flow occurring in a capillary is modified when its charged surfaces are coated by charged polymers. The theoretical treatment is based on a three dimensional model consisting of a ternary fluid-mixture, representing the solvent and two species for the ions, confined between two parallel charged plates decorated by a fixed array of scatterers representing the polymer coating. The electro-osmotic flow, generated by a constant electric field applied in a direction parallel to the plates, is studied numerically by means of Lattice Boltzmann simulations. In order to gain further understanding we performed a simple theoretical analysis by extending the Stokes-Smoluchowski equation to take into account the porosity induced by the polymers in the region adjacent the walls. We discuss the nature of the velocity profiles by focusing on the competing effects of the polymer charges and the frictional forces they exert. We show evidence of the flow reduction and of the flow inversion phenomenon when the polymer charge is opposite to the surface charge. By using the density of polymers and the surface charge as control variables, we propose a phase diagram that discriminates the direct and the reversed flow regimes and determine its dependence on the ionic concentration.Comment: 15 pages, 6 figures in Physical Chemistry Chemical Physics, 201

Market-based Investment in Electricity Transmission Networks: Controllable Flow

This paper discusses unregulated market-based electricity transmissio

Positivity Constraints on Anomalies in Supersymmetric Gauge Theories

The relation between the trace and R-current anomalies in supersymmetric theories implies that the U$(1)_RF^2$, U$(1)_R$ and U$(1)_R^3$ anomalies which are matched in studies of N=1 Seiberg duality satisfy positivity constraints. Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov $c$-theorem. These constraints are tested in a large number of N=1 supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R-current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient, $a_{UV}-a_{IR}$, is always positive, as conjectured by Cardy.Comment: latex, 36 page