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:**Motivated by recent evidence indicating that Quantum Einstein Gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term $(R^2)$. The beta-functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the $R^2$-coupling are computed explicitly. The fixed point (FP) properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian FP predicted by the latter is found to generalize to a FP on the enlarged theory space. In order to test the reliability of the $R^2$-truncation near this FP we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a suprisingly high precision. Due to the consistency of the results it appears increasingly unlikely that the non-Gaussian FP is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and ``asymptotically safe''. We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the $R^2$-truncation, the investigation of the FP is not afflicted with this problem. Also the Gaussian FP of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding FP on the enlarged theory space.Physical review D: Particles and fields 06/2002; - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition. Comment: 15 pagesEuropean Physical Journal C 07/2010; · 5.25 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study one-flavor QCD at finite temperature and chemical potential using the functional renormalization group. We discuss the chiral phase transition in QCD and its order with its underlying mechanism in terms of quarks and gluons and analyze the dependence of the phase transition temperature on small quark chemical potentials. Our result for the curvature of the phase boundary at small quark chemical potential relies on only a single input parameter, the value of the strong coupling at the Z mass scale. Comment: 49 pages, 3 figures; references added and discussion expanded (matches Eur. Phys. J. C version)European Physical Journal C 10/2008; · 5.25 Impact Factor

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