Existence of a weak-disorder non-Fermi liquid fixed point in the hydrodynamic regime of two-dimensional nematic quantum criticality

Role of quenched randomness in metallic quantum criticality is one of the long standing problems in condensed matter physics. An aspect of the fundamental difficulties lies in the fact that such nonmagnetic disorders lead effective interactions between abundant soft modes near the Fermi surface to be drastically enhanced particularly in the diffusive regime, where the perturbative framework does not work. Here, we revisit the problem of dirty quantum critical metals in a different angle, focusing on the hydrodynamic regime instead of the diffusive regime near the non-Fermi liquid quantum critical point. More concretely, we study effects of mutual correlations between quantum critical nematic fluctuations and weak localization corrections, and show the existence of a weak-disorder non-Fermi liquid fixed point, based on the renormalization group (RG) analysis up to the two-loop order. The two-loop order RG analysis suggests that the absence of quantum coherence in two-particle composite excitations weakens the role of weak localization corrections and allows a weakly disordered non-Fermi liquid metallic state in the hydrodynamic regime of the nematic quantum critical point. Although this dirty non-Fermi liquid metallic state may not be the true infrared stable fixed point at zero temperature, expected to be characterized by the diffusive Ohmic regime, we argue that this weak-disorder non-Fermi liquid metallic fixed point would govern the region of an intermediate energy scale, described by effective hydrodynamics of nematic quantum criticality. In this respect we believe that this research would be an important step in understanding the $T-$linear electrical resistivity as a characteristic feature of non-Fermi liquids and the origin of unconventional superconductivity from effective hydrodynamics of quantum criticality

U(1)_R mediation from the flux compactification in six dimensions

We consider a supersymmetric completion of codimension-two branes with nonzero tension in a 6D gauged supergravity. As a consequence, we obtain the football solution with 4D Minkowski space as a new supersymmetric background that preserves 4D N=1 SUSY. In the presence of brane multiplets, we derive the 4D effective supergravity action for the football background and show that the remaining modulus can be stabilized by a bulk non-perturbative correction with brane uplifting potentials at a zero vacuum energy. We find that the U(1)_R mediation can be a dominant source of SUSY breaking for a brane scalar with nonzero R charge.Comment: 3 pages, no figures, to appear in the proceedings of the 16th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY-2008), Seoul, Korea, 16-21 June, 200

Product imitation and policies of a developing country

The first chapter sets up the basic model of North-South trade. North innovates new variety of products and South imitates the old varieties that previously innovated and produced in the North. South has to invest R&D labor, which reduces the southern production cost to be able to compete in the market. The second chapter considers two industrial policies of South, R&D subsidy and entry subsidy to imitators. The effects of the subsidy depend on the unit cost gap between the North and the South. If the cost gap turned out to be narrow, zero R&D subsidy with a small subsidy to entry can raise the welfare of the southern consumers. If the cost gap is wide so that the southern firms can charge the optimal unconstrained monopoly price that, given demand assumptions, is a fixed mark up over the unit cost, the optimal R&D subsidy is positive. This subsidy raises the consumption of imitation varieties but reduces the number of the varieties. The last chapter is an empirical study that investigates the role of exchange rate on the trade flows. The bilateral data between U.S. and Canada are disaggregated into five end-use categories. Co-integration among the trade flow of each category, its relative price and the relative income of the two countries is tested to see if those variables maintained any long-run equilibrium relationship. Also short-run dynamics are checked through error correction model to measure how much the real exchange rates or the relative prices influence the trade flows