Renormalization of the Topological Charge in Yang-Mills Theory

The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological interaction, quantum effects due to the gauge bosons lead to a finite multiplicative renormalization of the theta--parameter while fermions give rise to an additional shift of theta. A truncated form of an exact renormalization group equation is used to study the scale dependence of the theta--parameter. Possible implications for the strong CP--problem of QCD are discussed.Comment: 31 pages, late

Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation

The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative \Fbeta-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4$. The resulting renormalization group trajectories are classified and their physical relevance is discussed. The non-trivial fixed point which, if present in the exact theory, might render Quantum Einstein Gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.Comment: 58 pages, latex, 24 figure

The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity

We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the ?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to appear in General Relativity and Gravitatio

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

Running Gauge Coupling in Asymptotically Safe Quantum Gravity

We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.Comment: 27 page

Density-functional theory investigation of oxygen adsorption at Pd(11N)(N=3,5,7) vicinal surfaces

We present a density-functional theory study addressing the on-surface adsorption of oxygen at the Pd(11N) (N =3,5,7) vicinal surfaces, which exhibit (111) steps and (100) terraces of increasing width. We find the binding to be predominantly governed by the local coordination at the adsorption site. This leads to very similar bonding properties at the threefold step sites of all three vicinal surfaces, while the binding at the central fourfold hollow site in the four atomic row terrace of Pd(117) is already very little disturbed by the presence of the neighboring steps.Comment: 9 pages including 4 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm

Metastable precursors during the oxidation of the Ru(0001) surface

Using density-functional theory, we predict that the oxidation of the Ru(0001) surface proceeds via the accumulation of sub-surface oxygen in two-dimensional islands between the first and second substrate layer. This leads locally to a decoupling of an O-Ru-O trilayer from the underlying metal. Continued oxidation results in the formation and stacking of more of these trilayers, which unfold into the RuO_2(110) rutile structure once a critical film thickness is exceeded. Along this oxidation pathway, we identify various metastable configurations. These are found to be rather close in energy, indicating a likely lively dynamics between them at elevated temperatures, which will affect the surface chemical and mechanical properties of the material.Comment: 11 pages including 9 figures. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Infrared remote sensing of cometary parent volatiles from the ground, air, and space

A balanced view of the present generation of infrared instruments for cometary compositional studies is presented. Ground-based instruments are compared with airborne and spaceborne capabilities. An attempt to give examples of the unique science achievable with each is made, and particular emphasis is on the unique aspects of a dedicated Cometary Composition Telescope in earth orbit for investigating the chemical and structural heterogeneity of the cometary nucleus