AdS/CFT Correspondence and Quotient Space Geometry

We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a fairly generic discrete group $\Gamma$ acting isometrically on $AdS_{d+1}$. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary ${\bf S}^{d}/\Gamma$ can affect the underlying physical spectrum. In particular, the conformal dimension of the most relevant operators in the boundary CFT can increase as $\Gamma$ becomes ``large''. This phenomenon also has a natural explanation in terms of the bulk supergravity theory. The scalar two-point function is computed using this quotient version of the AdS/CFT correspondence, which agrees with the expected result derived from conformal invariance of the boundary theory.Comment: 28 pages, Latex, no figures. Minor changes, version to appear in JHE

Coadjoint orbit of the virasoro group and the index theorem on Diff S1/S1

Abstract We use the methods of coadjoint orbits and the corresponding representations of the Virasoro group to formulate an index theorem for the BRST operator. A few concrete examples are set forth, one of them implies the vanishing theorem of Frenkel, Garland and Zukerman

Regenesis and quantum traversable wormholes

Recent gravity discussions of a traversable wormhole indicate that in holographic systems signals generated by a source could reappear long after they have dissipated, with the need of only performing some simple operations. In this paper we argue the phenomenon, to which we refer as "regenesis", is universal in general quantum chaotic many-body systems, and elucidate its underlying physics. The essential elements behind the phenomenon are: (i) scrambling which in a chaotic system makes out-of-time-ordered correlation functions (OTOCs) vanish at large times; (ii) the entanglement structure of the state of the system. The latter aspect also implies that the regenesis phenomenon requires fine tuning of the initial state. Compared to other manifestations of quantum chaos such as the initial growth of OTOCs which deals with early times, and a random matrix-type energy spectrum which reflects very large time behavior, regenesis concerns with intermediate times, of order the scrambling time of a system. We also study the phenomenon in detail in general two-dimensional conformal field theories in the large central charge limit, and highlight some interesting features including a resonant enhancement of regenesis signals near the scrambling time and their oscillations in coupling. Finally, we discuss gravity implications of the phenomenon for systems with a gravity dual, arguing that there exist regimes for which traversability of a wormhole is quantum in nature, i.e. cannot be associated with a semi-classical spacetime causal structure

Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing

In this paper, we establish some new central limit theorems for generalized U-statistics of dependent processes under some mild conditions. Such central limit theorems complement existing existing results available from both the econometrics literature and statistics literature. We then look at applications of the established results to a number of test problems in time series regression models.Central limit theorem; nonparametric specification; quadratic form; strict stationarity; stochastic process

When Globalization Meets Urbanization: Labor Market Reform, Income Inequality, and Economic Growth in the People's Republic of China

The development path that the People's Republic of China (PRC) has been following during the past thirty years has led to both internal and external economic imbalances, and is now greatly challenged by the global crisis. This unbalanced growth path was primarily a result of the PRC's labor market reform which took the years of the mid-1990s as its turning point. Before the mid-1990s, the scale of rural-to-urban migration was limited, but it has grown dramatically since then. 1996 also saw drastic employment restructuring in urban areas of the PRC. Labor market reform, accompanied by the foreign exchange system reform in 1994, confirmed the PRC's comparative advantage of low labor cost, and therefore further increased the PRC's reliance on exports. However, the increased income disparity that resulted from the labor market reform may jeopardize sustainable growth if no adjustment is made. To sustain the high economic growth, especially in face of the current crisis, the PRC needs to adjust its reform and development strategies to promote income equality.china labor market unemployment; china income inequality; china economic growth crisis

Coupling of Electronic and Nuclear Degrees of Freedom in Diatomic Molecules: A Quantum Defect Study.

The coupling of electronic and nuclear degrees of freedom in electron scattering from a homonuclear diatomic molecule has been studied using the frame transformation method in conjunction with the multichannel quantum defect theory (MQDT). Exploration of non-adiabatic effects resulting from large electron-molecule distances, resonances, and dissociation shows that the interconversion of energy between electronic and nuclear motion takes place mainly in the vicinity of the molecular target where the outermost electron couples strongly to the nuclei. MQDT enables us to describe these effects based on a body-frame quantum defect function, which can be obtained either from a short-range ab initio calculation (using Born-Oppenheimer approximation) or by fitting to the experimental data. This function thus provides sufficient information to characterize wavefunctions in asymptotic regions where the electron-molecule system may decay into different fragments (either the electron leaves the target, or else the two nuclei dissociate). The frame transformation method serves as a vehicle to convert the body-frame scattering parameter into laboratory-frame observables. We discuss two types of frame transformation methods for describing rovibrational coupling in this work. An energy-independent frame transformation is shown to be accurate enough to describe processes when the collision time of the scattering electron is negligible compared to the typical time for nuclear motion (i.e., when the energy dependence of the quantum defect is weak). In order to describe resonances (where the electron can be temporarily captured by the molecular target), we formulate an energy-dependent frame transformation which explicitly includes the energy dependence in the frame transformation without invoking any electron-molecule compound states. Finally, we make a preliminary study of processes involving competition between ionization and dissociation. Short-range rovibrational coupling is shown to govern such processes as well, for one class of molecular photoabsorption processes

Double occupancies in confined attractive fermions on optical lattices

We perform a numerical study of a one-dimensional Fermion-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The $\rho-U/t$ phase diagram is shown for the systems of attractive interactions ($\rho$ is the characteristic density and $U/t$ the interaction strength scaled in units of the hopping parameter.). We study the double occupancy, the local central density and their derivatives. Their roles are discussed in details in detecting the composite phases induced by the trapping potential.Comment: 4 pages, 4 figures, submitte