Abstract
Gravity is perhaps the most intriguing force in nature. Unlike the other fundamental interactions, gravity is embodied in the curvature of the very arena in which all natural processes occur. It is the presence of matter in the universe that tells the geometry of space-time how it should curve and warp.
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Notes
- 1.
for simplicity we assume there are no marginal directions.
References
Kadanoff, L. (1966). Scaling laws for Ising models near T(c). Physics, 2, 263–272.
Wilson, K. G., & Kogut, J. B. (1974). The renormalization group and the epsilon expansion. Physics Report, 12, 75–200.
Wilson, K. (1975). The renormalization group: Critical phenomena and the kondo problem. Reviews of Modern Physics, 47(4), 773–840.
Weinberg, S. (1979). Ultraviolet divergences in quantum theories of gravity. In S. W. Hawking & W. Israel (Eds.), General Relativity.
Niedermaier, M., & Reuter, M. (2006). The asymptotic safety scenario in quantum gravity. Living Reviews in Relativity, 9, 5.
Niedermaier, M. (2007). The asymptotic safety scenario in quantum gravity: An introduction. Classical and Quantum Gravity, 24, R171–230.
Percacci, R. (2007). Asymptotic Safety. In D. Oriti (Ed.), Approaches to quantum gravity: towards a new understanding of space, time and matter. Cambridge: University Press.
Litim, D. F. (2008). Fixed points of quantum gravity and the renormalisation group. In Proceedings of Workshop on from Quantum to Emergent Gravity: Theory and phenomenology.
Reuter, M. & Saueressig, F. (2007). Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity.
Litim, D. F. (2004). Fixed points of quantum gravity. Physical Review Letters, 92, 201301.
Litim, D. F. (2001). Optimized renormalization group flows. Physical Review, D64, 105007.
Litim, D. F. (2006). On fixed points of quantum gravity. AIP Conference Proceedings, 841, 322–329.
Gastmans, R., Kallosh, R., & Truffin, C. (1978). Quantum gravity near two-dimensions. Nuclear Physics, B133, 417.
Kawai, H., & Ninomiya, M. (1990). Renormalization group and quantum gravity. Nuclear Physics, B336, 115.
Kawai, H., Kitazawa, Y., & Ninomiya, M. (1996). Renormalizability of quantum gravity near two-dimensions. Nuclear Physics, B467, 313–331.
Smolin, L. (1982). A fixed point for quantum gravity. Nuclear Physics, B208, 439.
Tomboulis, E. (1977). 1/N expansion and renormalization in quantum gravity. Physics Letters, B70, 361.
Wetterich, C. (1993). Exact evolution equation for the effective potential. Physics Letters, B301, 90–94.
Reuter, M. (1998). Nonperturbative evolution equation for quantum gravity. Physical Review, D57, 971–985.
Lauscher, O., & Reuter, M. (2002c). Ultraviolet fixed point and generalized flow equation of quantum gravity. Physical Review, D65, 025013.
Souma, W. (1999). Non-trivial ultraviolet fixed point in quantum gravity. Progress of Theoretical Physics, 102, 181–195.
Reuter, M., & Saueressig, F. (2002). Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation. Physical Review, D65, 065016.
Fischer, P., & Litim, D. F. (2006a). Fixed points of quantum gravity in extra dimensions. Physics Letters, B638, 497–502.
Fischer, P., & Litim, D. F. (2006b). Fixed points of quantum gravity in higher dimensions. AIP Conference Proceedings, 861, 336–343.
Lauscher, O., & Reuter, M. (2002b). Is quantum Einstein gravity nonperturbatively renormalizable? Classical and Quantum Gravity, 19, 483–492.
Lauscher, O., & Reuter, M. (2002a). Flow equation of quantum Einstein gravity in a higher- derivative truncation. Physical Review, D66, 025026.
Codello, A., & Percacci, R. (2006). Fixed points of higher derivative gravity. Physical Review Letters, 97, 221301.
Benedetti, D., Machado, P. F., & Saueressig, F. (2009a). Asymptotic safety in higher-derivative gravity. Modern Physics Letters, A24, 2233–2241.
Benedetti, D., Machado, P. F., & Saueressig, F. (2009b). Four-derivative interactions in asymptotically safe gravity.
Benedetti, D., Machado, P. F., & Saueressig, F. (2010). Taming perturbative divergences in asymptotically safe gravity. Nuclear Physics, B824, 168–191.
Saueressig, F., Groh, K., Rechenberger, S., and Zanusso, O. (2011). Highederivative gravity from the universal renormalization group machine. PoS, EPS-HEP2011 (p. 124).
Eichhorn, A., & Gies, H. (2010). Ghost anomalous dimension in asymptotically safe quantum gravity. Phys. Rev., D81, 104010.
Eichhorn, A., Gies, H., & Scherer, M. M. (2009). Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity. Phys. Rev., D80, 104003.
Groh, K., & Saueressig, F. (2010). Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity. J. Phys., A43, 365403.
Bonanno, A., & Reuter, M. (2005a). Proper time flow equation for gravity. JHEP, 02, 035.
Bonanno, A., & Reuter, M. (2005b). Proper-time regulators and RG flow in QEG. AIP Conf. Proc., 751, 162–164.
Daum, J.-E., & Reuter, M. (2012). Renormalization group flow of the holst action. Physical Letters, B710:215–218 (5 pages, 1 figure).
Daum, J.-E., & Reuter, M. (2011a). Running immirzi parameter and asymptotic safety. Germany: University of Mainz.
Harst, U., & Reuter, M. (2012). The ’Tetrad only’ theory space: nonperturbative renormalization flow and asymptotic safety. Journal of High Energy Physics, 1205, 45 (10 figures).
Manrique, E., Reuter, M., & Saueressig, F. (2010b). Matter induced bimetric actions for gravity. Annals of Physics, 326(2), 440–462.
Manrique, E., Reuter, M., & Saueressig, F. (2010a). Bimetric renormalization group flows in quantum Einstein gravity. Annals of Physics 326:463–485.
Dou, D., & Percacci, R. (1998). The running gravitational couplings. Classical Quantum Gravity, 15, 3449–3468.
Percacci, R., & Perini, D. (2003a). Asymptotic safety of gravity coupled to matter. Physical Review, D68, 044018.
Percacci, R., & Perini, D. (2003b). Constraints on matter from asymptotic safety. Physical Review, D67, 081503.
Daum, J.-E., Harst, U., & Reuter, M. (2010b). Running gauge coupling in asymptotically safe quantum gravity. Journal of High Energy Physics, 1001, 084.
Daum, J.-E., Harst, U., & Reuter, M. (2010a). Non-perturbative QEG corrections to the Yang-Mills beta function. General Relativity and Gravitation.
Eichhorn, A. (2012). Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario. Physical Review D86:10.
Eichhorn, A., & Gies, H. (2011). Light fermions in quantum gravity. New Journal of Physics, 13, 125012.
Harst, U. & Reuter, M. (2011). QED coupled to QEG. Germany: University of Mainz.
Narain, G., & Percacci, R. (2010). Renormalization group flow in scalar-tensor theories. I Classical Quantum Gravity, 27, 075001.
Narain, G., & Rahmede, C. (2010). Renormalization group flow in scalar-tensor theories. II Classical Quantum Gravity, 27, 075002.
Vacca, G., & Zanusso, O. (2010). Asymptotic safety in einstein gravity and scalar-fermion matter. Physical Review Letters, 105, 231601.
Codello, A., Percacci, R., & Rahmede, C. (2008). Ultraviolet properties of f(R)-gravity. International Journal of Modern Physics, A23, 143–150.
Machado, P. F., & Saueressig, F. (2008). On the renormalization group flow of f(R)-gravity. Physical Review, D77, 124045.
Codello, A., Percacci, R., & Rahmede, C. (2009). Investigating the ultraviolet properties of gravity with a wilsonian renormalization group equation. Annals of Physics, 324, 414–469.
Reuter, M., & Weyer, H. (2009a). Background independence and asymptotic safety in conformally reduced gravity. Physical Review, D79, 105005.
Reuter, M., & Weyer, H. (2009b). Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of diffeomorphism invariance. Physical Review, D80, 025001.
Reuter, M., & Weyer, H. (2009c). The role of Background independence for asymptotic safety in quantum Einstein gravity. General Relativity and Gravitation, 41, 983–1011.
Daum, J.-E., & Reuter, M. (2009). Effective potential of the conformal factor: gravitational average action and dynamical triangulations. Advanced Science Letters, 2, 255–260.
Machado, P. F., & Percacci, R. (2009). Conformally reduced quantum gravity revisited. Physical Review, D80, 024020.
Daum, J.-E. and Reuter, M. (2011b). The Effective Potential of the Conformal Factor in Quantum Einstein Gravity. PoS, CLAQG08 (p. 013).
Demmel, M., Saueressig, F., and Zanusso, O. (2012). Fixed-Functionals of three-dimensional Quantum Einstein Gravity.
Percacci, R. (2011b). Renormalization group flow of Weyl invariant dilaton gravity. New Journal of Physics, 13:125013 (5 pages).
Percacci, R. (2006). Further evidence for a gravitational fixed point. Phys. Rev., D73, 041501.
Donkin, I. & Pawlowski, J. M. (2012). The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows (p. 23) (13 figures).
Litim, D. F., Percacci, R., & Rachwal, L. (2012). Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization. Physical Letters B710:472–477 (6 pages, 1 figure).
Litim, D. & Satz, A. (2012). Limit cycles and quantum gravity. College Park: University of Maryland.
Christiansen, N., Litim, D. F., Pawlowski, J. M., & Rodigast, A. (2012). Fixed points and infrared completion of quantum gravity.
Forgacs, P., & Niedermaier, M. (2002). A Fixed point for truncated quantum Einstein gravity. Journal of High Energy Physics, 12, 9.
Niedermaier, M., & Samtleben, H. (2000). An algebraic bootstrap for dimensionally reduced quantum gravity. Nuclear Physics, B579, 437–491.
Niedermaier, M. (2003). Dimensionally reduced gravity theories are asymptotically safe. Nuclear Physics, B673, 131–169.
Niedermaier, M. (2002). On the renormalization of truncated quantum Einstein gravity. Journal of High Energy Physics, 0212, 066.
Niedermaier, M. (2010). Gravitational fixed points and asymptotic safety from perturbation theory. Nuclear Physics, B833, 226–270.
Niedermaier, M. (2011). Can a nontrivial gravitational fixed point be identified in perturbation theory? PoS. Classical Quantum Gravity, 08, 005.
Niedermaier, M. R. (2009). Gravitational Fixed Points from perturbation theory. Physical Review Letters, 103, 101303.
Weinberg, S. (2010). Asymptotically safe inflation. Physical Review, D81, 083535.
Bonanno, A., & Reuter, M. (2002). Cosmology with self-adjusting vacuum energy density from a renormalization group fixed point. Physical Letters, B527, 9–17.
Bonanno, A. & Reuter, M. (2002). Cosmology of the planck era from a renormalization group for quantum gravity. Physical Review D 65, 043508.
Bonanno, A., Contillo, A., & Percacci, R. (2011). Inflationary solutions in asymptotically safe f(R) theories. Classical Quantum Gravity, 28, 145026.
Bonanno, A. & Reuter, M. (2010). Entropy Production during Asymptotically Safe Inflation 13(1):274–292.
Bonanno, A. (2011a). Astrophysical implications of the asymptotic safety scenario in quantum gravity. Classical Quantum Gravity (Pos), 08, 008.
Contillo, A. (2011a). Evolution of cosmological perturbations in an RG-driven inflationary scenario. Physical Review, D83, 085016.
Contillo, A. (2011b). Inflation in asymptotically safe f(R) theory. Journal of Physics: Conference Series, 283, 012009.
Hindmarsh, M., Litim, D., & Rahmede, C. (2011). Asymptotically safe cosmology. Journal of Cosmology and Astroparticle Physics, 1107, 019.
Hong, S. E., Lee, Y. J., & Zoe, H. (2011). The Possibility of Inflation in Asymptotically Safe Gravity 36(1–3), 178–186.
Koch, B., & Ramirez, I. (2011). Exact renormalization group with optimal scale and its application to cosmology. Classical Quantum Gravity, 28, 055008.
Tye, S. H. H., & Xu, J. (2010). Comment on asymptotically safe inflation. Physical Review, D82, 127302.
Bonanno, A., & Reuter, M. (2000). Renormalization group improved black hole spacetimes. Physical Review, D62, 043008.
Bonanno, A., & Reuter, M. (2006). Spacetime structure of an evaporating black hole in quantum gravity. Physical Review, D73, 083005.
Reuter, M., & Tuiran, E. (2011). Quantum gravity effects in the kerr spacetime. Physical Review D 83:044041.
Falls, K., Litim, D. F., & Raghuraman, A. (2012b). Black holes and asymptotically safe gravity. International Journal of Modern Physics, A27, 1250019.
Cai, Y.-F., & Easson, D. A. (2010). Black holes in an asymptotically safe gravity theory with higher derivatives. Journal of Cosmology and Astroparticle Physics 1009:002.
Burschil, T., & Koch, B. (2010). Renormalization group improved black hole space-time in large extra dimensions. Zh.Eksp. Teor. Fiz. 92:219–225 2010. Jounal of Experimental and Theoretical Physics Letters, 92, 193–199.
Gies, H. (2006). Introduction to the functional RG and applications to gauge theories.
Berges, J., Tetradis, N., & Wetterich, C. (2002). Nonperturbative renormalization flow in quantum field theory and statistical physics. Physical Report, 363, 223–386.
Pawlowski, J. M. (2007). Aspects of the functional renormalisation group. Annals of Physics, 322, 2831–2915.
Polonyi, J. (2003). Lectures on the functional renormalization group method. The Central European Journal of Physics, 1, 1–71.
Rosten, O. J. (2012). Fundamentals of the exact renormalization group. Physical Report, 511, 177–272.
Wetterich, C. (1991). Average action and the renormalization group equations. Nuclear Physics, B352, 529–584.
Litim, D. F. (2000). Optimization of the exact renormalization group. Physical Letters, B486, 92–99.
Stevenson, P. M. (1981). Optimized perturbation theory. Physical Review Letters, D23, 2916.
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Falls, K. (2013). The Renormalisation Group. In: Asymptotic Safety and Black Holes. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01294-0_2
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