International Journal of Modern Physics A

We discuss some of the issues arising when considering asymptotically de Sitter space–times and attempts to address them. Our development begins at the classical level where several initial value problems are discussed and ends with several proposals for holography in asymptotically de Sitter space–times. Throughout the paper we give a review of some basic notions such as the geometry of Schwarzschild–de Sitter black hole, the Nariai limit and quantum field theory in a fixed de Sitter background. We also briefly discuss some semiclassical aspects such as the nucleation of black holes and the Hartle–Hawking wavefunctional. We end by giving an overview of some open questions. An emphasis is placed on the differences between a static patch observer confined to live in a thermal cavity and the metaobserver who has access to a finite region of the future boundary.

In the full type IIB open superstring setup, we show that there exists a vertex operator, denoted by V_L, whose renormalization reproduces the same anomalous dimension matrix that was obtained by Minahan and Zarembo (MZ) [J. High Energy Phys. 0303, 013 (2003)]. The vertex operator is a gauge singlet, and has the same SO(6) index structure as the operator used by MZ. To obtain the SYM anomalous dimensions, one of the key ingredients is the non-abelianization of the nonlinear sigma model action in a D-brane background. Park [Phys. Lett. B 660, 583 (2008)] conjectured that quantum effects of open strings on a stack of D-branes should generate the curvature. Even though the conjecture had passed a few consistency checks, the role of the higher order curvature terms has remain mostly unobserved until now. By choosing a special form of the non-abelianized counter vertex, V_G, we show that the SYM result is reproduced. We comment on fermionic completion of V_L and on how the special form of the non-Abelian vertex V_G may arise.

The RG flow equation of various transport quantities are studied in arbitrary space–time dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the flow equation of the conductivity at the horizon for the DBI action reproduces naturally the leading order result of Hartnoll et al. [J. High Energy Phys. 04, 120 (2010)]. Motivated by the result of van der Marel et al. [Science 425, 271 (2003], we studied, analytically, the conductivity versus frequency plane by dividing it into three distinct parts: ω < T, ω > T and ω ≫ T. In order to compare, we choose (3+1)-dimensional bulk space–time for the computation of the conductivity. In the ω < T range, the conductivity does not show up the Drude like form in any space–time dimensions. In the ω > T range and staying away from the horizon, for the DBI action with unit dynamical exponent, nonzero magnetic field and charge density, the conductivity goes as ω^-2/3, whereas the phase of the conductivity, goes as, arctan(Im σ^xx/Re σ^xx) = π/6 and arctan(Im σ^xy/Re σ^xy) = -π/3. There exists a universal quantity at the horizon that is the phase angle of conductivity, which either vanishes or an integral multiple of π. Furthermore, we calculate the temperature dependence to the thermoelectric and the thermal conductivity at the horizon. The charge diffusion constant for the DBI action is studied.

The top quark pair production and decay are considered in the framework of the smeared-mass unstable particles model. The results for total and differential cross-sections in vicinity of threshold are in good agreement with the previous ones in the literature. The strategy of calculations of the higher order corrections in the framework of the model is discussed. Suggested approach significantly simplifies calculations compared to the standard perturbative one and can serve as a convenient tool for fast and precise preliminary analysis of processes involving intermediate timelike top quark exchanges in the near-threshold region.

The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials V_{A, B, ext}(x), obtained from a conventional Morse potential V_{A-1, B}(x) by the addition of a bound state below the spectrum of the latter, is reobtained. More importantly, the existence of another family of extended potentials, strictly isospectral to V_{A+1, B}(x), is pointed out for a well-chosen range of parameter values. Although not shape invariant, such extended potentials exhibit a kind of "enlarged" shape invariance property, in the sense that their partner, obtained by translating both the parameter A and the degree m of the polynomial arising in the denominator, belongs to the same family of extended potentials. The point canonical transformation connecting the radial oscillator to the Morse potential is also applied to exactly solvable rationally-extended radial oscillator potentials to build quasi-exactly solvable rationally-extended Morse ones.

We formulate a modified theory of gravity and equivalent second-order gravity theory for a Lagrangian containing R and term in spatially homogeneous and isotropic background. The term in the action can be thought of as equivalent to a source term in Einstein's gravity, which can be assumed to be equivalent with a perfect fluid characterized by density ρ and pressure p. The pressure p is a function of ρ, scale factor a and the curvature parameter R. We present a few analytical solutions of evolution equation for deceleration parameter q as a function of p and ρ.