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

Optical spectroscopy of molecular junctions: Nonequilibrium Green's functions perspective

We consider optical spectroscopy of molecular junctions from the quantum transport perspective when radiation field is quantized and optical response of the system is simulated as photon flux. Using exact expressions for photon and electronic fluxes derived within the nonequilibrium Green function (NEGF) methodology and utilizing fourth order diagrammatic perturbation theory in molecular coupling to radiation field we perform simulations employing realistic parameters. Results of the simulations are compared to the bare perturbation theory (PT) usually employed in studies on nonlinear optical spectroscopy to classify optical processes. We show that the bare PT violates conservation laws, while flux conserving NEGF formulation mixes optical processes.Comment: 10 pages, 6 figure

Simulation of optical response functions in molecular junctions

We discuss theoretical approaches to nonlinear optical spectroscopy of molecular junctions. Optical response functions are derived in the form convenient for implementation of Green function techniques, and their expressions in terms of pseudoparticle nonequilibrium Green functions are proposed. The formulation allows to account for both intra-molecular interactions and hybridization of molecular states due to coupling to contacts. Two-dimensional optical spectroscopy in junctions is considered as an example.Comment: 11 pages, 7 figure

Regioselective Formation of α-Vinylpyrroles from the Ruthenium-Catalyzed Coupling Reaction of Pyrroles and Terminal Alkynes Involving C–H Bond Activation

The cationic ruthenium catalyst Ru3(CO)12/NH4PF6 was found to be highly effective for the intermolecular coupling reaction of pyrroles and terminal alkynes to give gem-selective α-vinylpyrroles. The carbon isotope effect on the α-pyrrole carbon and the Hammett correlation from a series of para-substituted N-arylpyrroles (ρ = −0.90) indicate a rate-limiting C−C bond formation step of the coupling reaction