Geometric models of twisted differential K-theory I

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and we use twisted vector bundles with connection as cocycles. The model we construct satisfies the axioms of Kahle and Valentino, including functoriality, naturality of twists, and the hexagon diagram. This paper confirms a long-standing hypothetical idea that twisted vector bundles with connection define twisted differential K-theory

The Soybean

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Deformations of Lifshitz holography with the Gauss-Bonnet term in (n+1n+1) dimensions

We investigate deformations of Gauss-Bonnet-Lifshitz holography in $(n+1)$ dimensional spacetime. Marginally relevant operators are dynamically generated by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed Gauss-Bonnet-Lifshitz spacetimes via a holographic picture. To admit (non-trivial) sub-leading orders of the asymptotic solution for the marginal mode, we find that the value of the dynamical critical exponent $z$ is restricted by $z= n-1-2(n-2) \tilde{\alpha}$, where $\tilde{\alpha}$ is the (rescaled) Gauss-Bonnet coupling constant. The generic black hole solution, which is characterized by the horizon flux of the vector field and $\tilde{\alpha}$, is obtained in the bulk, and we explore its thermodynamic properties for various values of $n$ and $\tilde{\alpha}$.Comment: 40 pages, 13 figure

Deformations of Lifshitz Holography in (n+1)(n+1)-dimensions

We investigate deformations of Lifshitz holography in $(n+1)$ dimensional spacetime. After discussing the situation for general Lifshitz scaling symmetry parameter $z$, we consider $z=n-1$ and the associated marginally relevant operators. These operators are dynamically generated by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed Lifshitz spacetimes via a holographic picture. We obtain renormalization group flow at finite temperature from UV Lifshitz to IR AdS, and evaluate how physical quantities such as the free energy density and the energy density depend on $\log(\Lambda^z/T)$ in the quantum critical regime as $\Lambda^z/T \rightarrow 0$.Comment: 27 pages, 10 figures with multiple plot

Periodically Aligned Liquid Crystal: Potential application for projection displays

A nematic liquid crystal (NLC) layer with the anisotropy axis modulated at a fixed rate q in the transverse direction is considered. If the layer locally constitutes a half-wave plate, then the thin-screen approximation predicts 100% -efficient diffraction of normal incident wave. The possibility of implementing such a layer via anchoring at both surfaces of a cell with thickness L is studied as a function of parameter qL and threshold values of this parameter are found for a variety of cases. Distortions of the structure of director in comparison with the preferable ideal profile are found via numerical modeling. Freedericksz transition is studied for this configuration. Coupled-mode theory is applied to light propagation through such cell allowing to account for walk-off effects and effects of nematic distortion. In summary, this cell is suggested as a means for projection display; high efficiency is predicted.Comment: 25 pages, 6 figures, 1 tabl

Metal-insulator (fermion-boson)-crossover origin of pseudogap phase of cuprates I: anomalous heat conductivity, insulator resistivity boundary, nonlinear entropy

Among all experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which the high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator - bosonic metal - fermionic metal transitions.Comment: 13 pages, 3 figure