Fixed Points of Quantum Gravity and the Renormalisation Group

Proceedings of Science 10/2008;
Source: arXiv


We review the asymptotic safety scenario for quantum gravity and the role and implications of an underlying ultraviolet fixed point. We discuss renormalisation group techniques employed in the fixed point search, analyse the main picture at the example of the Einstein-Hilbert theory, and provide an overview of the key results in four and higher dimensions. We also compare findings with recent lattice simulations and evaluate phenomenological implications for collider experiments. Comment: 18 pages, 4 figures. Plenary talk. To appear in the proceedings of "From Quantum to Emergent Gravity: Theory and Phenomenology", June 11-15 2007, Trieste, Italy

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Available from: Daniel F. Litim, Sep 16, 2014
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    • "The main endeavors along this line were enumeration of the counter terms in the effective action [6] [7] [8] and the progress made in the asymptotically safe gravity [9] [10] [11] [12] [13]. It was established for 4D Einstein action that the divergences do not cancel except for one-loop; one faces proliferation of counter terms as the order of loop increases -which turns out to be typical of other gravity theories, and the theory loses its predictability. "
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    ABSTRACT: With the Hamiltonian and Lagrangian analyses in the ADM setup, it was observed in \cite{Park:2014tia} that the physical configuration space of the 4D Einstein-Hilbert action admits a three-dimensional description. Subsequently, a more mathematical picture of the reduction based on foliation theory was presented in \cite{Park:2014qoa}. In this work, we expand \cite{Park:2014qoa} by adding another mathematical ingredient - an element of jet bundle theory - and present a more systematic and refined account thereof.
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    • "Any results obtained from this can only be trusted at low energies as EH gravity is a low energy limit of any fundamental theory of quantum gravity. In [29] [30] however Functional renormalization group has been used to study the problem in the spirit of asymptotic safety scenario [31] [32] [33] [34] [35]. "
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    ABSTRACT: In this paper we study the coupled system of non-abelian gauge fields with higher-derivative gravity. Charge renormalization is investigated in this coupled system. It is found that the leading term in the gauge coupling beta function comes due to interaction of gauge fields with gravitons. This is shown to be a universal quantity in the sense that it doesn't depend on the gauge coupling and the gauge group, but may depend on the other couplings of the action (gravitational and matter). The coupled system is studied at one-loop. It is found that the leading term of gauge beta function is zero at one-loop in four dimensions. The effect of gauge fields on the running of gravitational couplings is investigated. The coupled system of gauge field with higher-derivative gravity is shown to satisfy unitarity when quantum corrections are taken in to account. Moreover, it is found that Newton constant goes to zero at short distances. In this renormalizable and unitary theory of gauge field coupled with higher-derivative gravity, the leading term of the gauge beta function, found to be universal for all gauge groups, is further studied in more detail by isolating it in the context of abelian gauge theories coupled with gravity in four dimensions. Using self-duality of abelian gauge theories in four dimensions, this term of the gauge beta function is shown to be zero to all loops. This is found to be independent of the gravity action, regularization scheme and gauge fixing condition. An explicit one-loop computation for arbitrary gravity action further demonstrates the vanishing of this term in the gauge beta function in four dimensions, independent of the regularization scheme and gauge fixing condition. Consequences of this are discussed.
    Journal of High Energy Physics 09/2013; 2013(10). DOI:10.1007/JHEP10(2013)203 · 6.11 Impact Factor
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    • "The running scale is t = ln k, and R k is the cutoff function. For further details we refer to the many general reviews [32] [33] [34] [35] [36] [37] and to the gravity-oriented ones [38] [39] [40] [41]. "
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    ABSTRACT: It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
    New Journal of Physics 07/2011; 14(1). DOI:10.1088/1367-2630/14/1/015005 · 3.56 Impact Factor
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