Article

# Renormalisation group flows for gauge theories in axial gauges

Journal of High Energy Physics (Impact Factor: 5.62). 02/2002; DOI: 10.1088/1126-6708/2002/09/049

Source: arXiv

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**ABSTRACT:**We study the 3d Ising universality class using the functional renormalization group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and antisymmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross correlations of scaling exponents, their dependence on dimensionality, and the numerical convergence of the derivative expansion. Collecting all available data from functional renormalization group studies to date, we estimate that systematic errors are in good agreement with findings from Monte Carlo simulations, ϵ-expansion techniques, and resummed perturbation theory.Physical review D: Particles and fields 04/2011; 83(8). - [Show abstract] [Hide abstract]

**ABSTRACT:**Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.Journal of High Energy Physics 12/2013; 2014(3). · 5.62 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short-distance physics is characterized by a nontrivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross-section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross-sections display a threshold, are suppressed in the Planckian, and reproduce the semiclassical result in the deep trans-Planckian region. Further implications are discussed.International Journal of Modern Physics A 04/2012; 27(05). · 1.13 Impact Factor

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