Impact of topology in foliated Quantum Einstein Gravity

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale-dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S^1xS^d. The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism. The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme. The phase diagrams show that this fixed point is connected to a classical regime through a crossover. In addition the flow may exhibit a regime of "gravitational instability", modifying the theory in the deep infrared. Our work complements earlier studies of the gravitational renormalization group flow on a background topology S^1xT^d and establishes that the flow is essentially independent of the background topology.Comment: 33 pages, 14 figure

On the scaling of composite operators in Asymptotic Safety

The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies non-trivial quantum corrections to the scaling dimensions of operators and correlation functions which are characteristic for the corresponding universality class. We use the composite operator formalism for the effective average action to derive an analytic expression for the scaling dimension of an infinite family of geometric operators $\int d^dx \sqrt{g} R^n$. We demonstrate that the anomalous dimensions interpolate continuously between their fixed point value and zero when evaluated along renormalization group trajectories approximating classical general relativity at low energy. Thus classical geometry emerges when quantum fluctuations are integrated out. We also compare our results to the stability properties of the interacting renormalization group fixed point projected to $f(R)$-gravity, showing that the composite operator formalism in the single-operator approximation cannot be used to reliably determine the number of relevant parameters of the theory.Comment: matches published versio

Chain transfer kinetics of acid/base switchable n-aryl- n-pyridyl dithiocarbamate RAFT agents in methyl acrylate, n-vinylcarbazole and vinyl acetate polymerization

This is an accepted manuscript of an article published by American Chemistry Society in Macromolecules on 14/05/2012, available online: https://doi.org/10.1021/ma300616g ©American Chemical Society. The accepted version of the publication may differ from the final published version.The structures of the "Z" and "R" substituents of a RAFT agent (Z-C(S)S-R) determine a RAFT agent's ability to control radical polymerization. In this paper we report new acid/base switchable N-aryl-N-pyridyl dithiocarbamates (R = -CH 2CN, Z = -N(Py)(Ar)) which vary in substituent at the 4-position of the aryl ring and the use of these to control molecular weight and dispersity. In their protonated form, the new RAFT agents are more effective in controlling polymerization of the more activated monomer, methyl acrylate (MA), whereas in their neutral form they provide more effective control of the polymerization of less activated monomers, N-vinyl carbazole (NVC) and vinyl acetate (VAc). For each polymerization, the apparent chain transfer coefficient (C trapp) shows a good correlation with Hammett parameters. Dithiocarbamates with more electron-withdrawing aryl ring substituents have the higher C trapp. This demonstrates the influence of polar effects on C trapp and supports the hypothesis that the activity of these RAFT agents is determined by the availability of the lone pair of the dithiocarbamate nitrogen.The authors gratefully acknowledge the Capability Development Fund of CSIRO Materials Science and Engineering for financial support.Published versio

One size fits all? High frequency trading, tick size changes and the implications for exchanges: market quality and market structure considerations

This paper offers a systematic review of the empirical literature on the implications of tick size changes for exchanges. Our focus is twofold: first, we are concerned with the market quality implications of a change in the minimum tick size. Second, we are interested in the implications of changes in the minimum tick size on market structure. We show that there is a large body of empirical literature that documents a decrease in transaction costs following a decrease in the minimum tick size. However, even though market liquidity increases, the incentive to provide market making activities decreases. We document a strong link between the minimum tick size regulations and the recent increase in high frequency trading activity. A smaller tick enhances the price discovery process. However, the question of how multiple tick size regimes affect market liquidity in a fragmented market remains to be answered. Finally, we identify topics for future research; we discuss the empirical literature on the minimum trade unit and the recent calls for a minimum resting time for quotes