A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions

The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three nonconformal solutions, given by remarkably simple (albeit nontrivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization group flows is discussed as well as several physical applications.Comment: LaTeX, 18 pages, no figure

One-loop f(R) Gravitational Modified Models

The one-loop quantisation of a general class of modified gravity models around a classical de Sitter background is presented. Application to the stability of the models is addressed.Comment: Latex, 8 pages, no figures. To appear in Journal of Physics A. Two references adde

Exact Renormalization Group and Running Newtonian Coupling in Higher Derivative Gravity

We discuss exact renormalization group (RG) in $R^2$-gravity using effective average action formalism. The truncated evolution equation for such a theory on De Sitter background leads to the system of nonperturbative RG equations for cosmological and gravitational coupling constants. Approximate solution of these RG equations shows the appearence of antiscreening and screening behaviour of Newtonian coupling what depends on higher derivative coupling constants.Comment: Latex file, 9 page

Bulk versus brane running couplings

A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is considered. It has been observed previously by Goldberger and Wise that in such a self-interacting scalar theory on the bulk with a conical singularity there is mixing of renormalization of 4d brane couplings with that of the bulk couplings. We study the influence of the running bulk couplings on the running of the 4d brane couplings. We find that bulk quantum effects may completely alter the running of brane couplings. In particular, the structure of the Landau pole may be drastically altered and non-asymptotically free running may turn into asymptotically safe (or free) behavior.Comment: 11 pages, no figures, REVTeX

Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary

The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the theory to second order in the scalar self-coupling pursued herein involves explicit calculations of up to third loop-order and reveals that, in addition to the renormalisation of the scalar self-coupling and scalar field, the removal of all divergences necessitates the introduction of conformally non-invariant counterterms proportional to $R\Phi^2$ and $K\Phi^2$ in the bare scalar action as well as counterterms proportional to $RK^2$, $R^2$ and $RK$ in the gravitational action. The substantial backreaction effects and their relevance to the renormalisation procedure are analysed.Comment: 25 pages, 1 figure. Minor elucidations in the Appendix regarding the cut-off $N_0$ and in p.4 regarding the gravitational action. Certain reference-related ommission corrected. To appear in Classical and Quantum Gravit

Dark Energy Dominance and Cosmic Acceleration in First Order Formalism

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation.Comment: 21 pages, LaTeX file, no figures. Replaced version to be published on Phys. Rev.

Strong correlation effects in single-wall carbon nanotubes

We present an overview of strong correlations in single-wall carbon nanotubes, and an introduction to the techniques used to study them theoretically. We concentrate on zigzag nanotubes, although universality dictates that much ofthe theory can also be applied to armchair or chiral nanotubes. We show how interaction effects lead to exotic low energy properties and discuss future directions for studies on correlation effects in nanotubes

Holographic entropy and brane FRW-dynamics from AdS black hole in d5 higher derivative gravity

Higher derivative bulk gravity (without Riemann tensor square term) admits AdS-Schwarzschild black hole as exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated Universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of 5-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. Cardy-Verlinde formula which expresses cosmological entropy as square root from other parameters and entropies is derived in $R^2$ gravity. The corresponding cosmological entropy bounds are briefly discussed.Comment: LaTeX file, 19 page

Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter

Two dimensional dilaton gravity interacting with a four-fermion model and scalars is investigated, all the coefficients of the Lagrangian being arbitrary functions of the dilaton field. The one-loop covariant effective action for 2D dilaton gravity with Majorana spinors (including the four-fermion interaction) is obtained, and the technical problems which appear in an attempt at generalizing such calculations to the case of the most general four-fermion model described by Dirac fermions are discussed. A solution to these problems is found, based on its reduction to the Majorana spinor case. The general covariant effective action for 2D dilaton gravity with the four-fermion model described by Dirac spinors is given. The one-loop renormalization of dilaton gravity with Majorana spinors is carried out and the specific conditions for multiplicative renormalizability are found. A comparison with the same theory but with a classical gravitational field is done.Comment: LaTeX, 25 pages, july 2