Asymptotically safe \(f(R)\)-gravity coupled to matter. I: The polynomial case. (English) Zbl 1398.83030
Summary: We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) arising within the framework of \(f(R)\)-gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields. Based on this setting we provide comprehensible estimates whose gravity-matter systems give rise to NGFPs suitable for rendering the theory asymptotically safe. The analysis employs an exponential split of the metric fluctuations and retains a 7-parameter family of coarse-graining operators allowing the inclusion of non-trivial endomorphisms in the regularization procedure. For vanishing endomorphisms, it is established that gravity coupled to the matter content of the standard model of particle physics and many beyond the standard model extensions exhibit NGFPs whose properties are strikingly similar to the case of pure gravity: there are two UV-relevant directions and the position and critical exponents converge rapidly when higher powers of the scalar curvature are included. Conversely, none of the phenomenologically interesting gravity-matter systems exhibits a stable NGFP when a Type II coarse graining operator is employed. Our analysis resolves this tension by demonstrating that the NGFPs seen in the two settings belong to different universality classes.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
Keywords:
quantum gravity; asymptotic safety; functional renormalization group; gravity-matter systemsReferences:
| [1] | Weinberg, S., (Hawking, S. W.; Israel, W., General Relativity: An Einstein Centenary Survey, (1979), Camb. Univ. Press Cambridge, UK) · Zbl 0424.53001 |
| [2] | Weinberg, S., (Cao, T. Y., Boston 1996, Conceptual foundations of quantum field theory, (2004), Camb. Univ. Press Cambridge, UK), 241, hep-th/9702027 |
| [3] | Niedermaier, M.; Reuter, M., Living Rev. Relativ., 9, 5, (2006) · Zbl 1255.83056 |
| [4] | Codello, A.; Percacci, R.; Rahmede, C., Ann. Physics, 324, 414, (2009) |
| [5] | Litim, D. F., Philos. Trans. R. Soc. Lond. Ser. A, 369, 2759, (2011) · Zbl 1228.82028 |
| [6] | R. Percacci, arXiv:1110.6389; R. Percacci, arXiv:1110.6389 |
| [7] | Reuter, M.; Saueressig, F., New J. Phys., 14, (2012) |
| [8] | Nagy, S., Ann. Physics, 350, 310, (2014) |
| [9] | Percacci, R., An introduction to covariant quantum gravity and asymptotic safety, (2017), World Scientific · Zbl 1368.81013 |
| [10] | Reuter, M., Phys. Rev. D, 57, 971, (1998), hep-th/9605030 |
| [11] | Souma, W., Progr. Theoret. Phys., 102, 181, (1999), hep-th/9907027 |
| [12] | Falkenberg, S.; Odintsov, S. D., Internat. J. Modern Phys. A, 13, 607, (1998), hep-th/9612019 |
| [13] | Reuter, M.; Saueressig, F., Phys. Rev. D, 65, (2002), hep-th/0110054 |
| [14] | Lauscher, O.; Reuter, M., Phys. Rev. D, 65, (2002), hep-th/0108040 |
| [15] | Litim, D. F., Phys. Rev. Lett., 92, (2004), hep-th/0312114 |
| [16] | Bonanno, A.; Reuter, M., J. High Energy Phys., 02, 035, (2005), hep-th/0410191 |
| [17] | Eichhorn, A.; Gies, H.; Scherer, M. M., Phys. Rev. D, 80, (2009) |
| [18] | Manrique, E.; Reuter, M., Ann. Physics, 325, 785, (2010) |
| [19] | Eichhorn, A.; Gies, H., Phys. Rev. D, 81, (2010) |
| [20] | Groh, K.; Saueressig, F., J. Phys. A, 43, (2010) |
| [21] | Manrique, E.; Reuter, M.; Saueressig, F., Ann. Physics, 326, 463, (2011) · Zbl 1210.83018 |
| [22] | Christiansen, N.; Litim, D. F.; Pawlowski, J. M.; Rodigast, A., Phys. Lett. B, 728, 114, (2014) · Zbl 1377.83030 |
| [23] | Codello, A.; D’Odorico, G.; Pagani, C., Phys. Rev. D, 89, (2014) |
| [24] | Christiansen, N.; Knorr, B.; Pawlowski, J. M.; Rodigast, A., Phys. Rev. D, 93, (2016) |
| [25] | Becker, D.; Reuter, M., Ann. Phys., 350, 225, (2014) · Zbl 1344.83024 |
| [26] | Falls, K., J. High Energy Phys., 01, 069, (2016) |
| [27] | Falls, K., Phys. Rev. D, 92, (2015) |
| [28] | Christiansen, N.; Knorr, B.; Meibohm, J.; Pawlowski, J. M.; Reichert, M., Phys. Rev. D, 92, (2015) |
| [29] | Gies, H.; Knorr, B.; Lippoldt, S., Phys. Rev. D, 92, (2015) |
| [30] | Benedetti, D., Gen. Relativity Gravitation, 48, 68, (2016) · Zbl 1381.83001 |
| [31] | Pagani, C.; Reuter, M., Phys. Rev. D, 95, (2017) |
| [32] | T. Denz, J.M. Pawlowski, M. Reichert, arXiv:1612.07315; T. Denz, J.M. Pawlowski, M. Reichert, arXiv:1612.07315 |
| [33] | Falls, K., Phys. Rev. D, 96, (2017) |
| [34] | Knorr, B.; Lippoldt, S., Phys. Rev. D, 96, (2017) |
| [35] | Lauscher, O.; Reuter, M., Phys. Rev. D, 66, (2002), hep-th/0205062 |
| [36] | Reuter, M.; Saueressig, F., Phys. Rev. D, 66, (2002), hep-th/0206145 |
| [37] | Codello, A.; Percacci, R., Phys. Rev. Lett., 97, (2006), hep-th/0607128 |
| [38] | Codello, A.; Percacci, R.; Rahmede, C., Internat. J. Modern Phys. A, 23, 143, (2008) |
| [39] | Machado, P. F.; Saueressig, F., Phys. Rev. D, 77, (2008) |
| [40] | Niedermaier, M. R., Phys. Rev. Lett., 103, (2009) |
| [41] | Benedetti, D.; Machado, P. F.; Saueressig, F., Modern Phys. Lett. A, 24, 2233, (2009) · Zbl 1175.83030 |
| [42] | Benedetti, D.; Machado, P. F.; Saueressig, F., Nuclear Phys. B, 824, 168, (2010) · Zbl 1196.83019 |
| [43] | Benedetti, D.; Machado, P. F.; Saueressig, F., AIP Conf. Proc., 1196, 44, (2009) |
| [44] | Benedetti, D.; Groh, K.; Machado, P. F.; Saueressig, F., J. High Energy Phys., 06, 079, (2011) · Zbl 1298.83042 |
| [45] | Rechenberger, S.; Saueressig, F., Phys. Rev. D, 86, (2012) |
| [46] | Ohta, N.; Percacci, R., Classical Quantum Gravity, 31, (2014) |
| [47] | K. Falls, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1301.4191; K. Falls, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1301.4191 |
| [48] | Benedetti, D., Europhys. Lett., 102, 20007, (2013) |
| [49] | Falls, K.; Litim, D. F.; Nikolakopoulos, K.; Rahmede, C., Phys. Rev. D, 93, (2016) |
| [50] | Eichhorn, A., J. High Energy Phys., 04, 096, (2015) |
| [51] | Ohta, N.; Percacci, R.; Vacca, G. P., Phys. Rev. D, 92, (2015) |
| [52] | K. Falls, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1607.04962; K. Falls, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1607.04962 |
| [53] | Falls, K.; Ohta, N., Phys. Rev. D, 94, (2016) |
| [54] | N. Christiansen, arXiv:1612.06223; N. Christiansen, arXiv:1612.06223 |
| [55] | Gonzalez-Martin, S.; Morris, T. R.; Slade, Z. H., Phys. Rev. D, 95, (2017) |
| [56] | Becker, D.; Ripken, C.; Saueressig, F., J. High Energy Phys., 12, 121, (2017) · Zbl 1383.83025 |
| [57] | Reuter, M.; Weyer, H., Phys. Rev. D, 80, (2009) |
| [58] | Benedetti, D.; Caravelli, F., J. High Energy Phys., JHEP, 10, 157, (2012), Erratum |
| [59] | Demmel, M.; Saueressig, F.; Zanusso, O., J. High Energy Phys., 11, 131, (2012) · Zbl 1397.83030 |
| [60] | Dietz, J. A.; Morris, T. R., J. High Energy Phys., 01, 108, (2013) · Zbl 1342.81339 |
| [61] | Bridle, I. H.; Dietz, J. A.; Morris, T. R., J. High Energy Phys., 03, 093, (2014) |
| [62] | Dietz, J. A.; Morris, T. R., J. High Energy Phys., 07, 064, (2013) |
| [63] | Demmel, M.; Saueressig, F.; Zanusso, O., J. High Energy Phys., 06, 026, (2014) · Zbl 1333.83017 |
| [64] | Demmel, M.; Saueressig, F.; Zanusso, O., Ann. Physics, 359, 141, (2015) |
| [65] | Demmel, M.; Saueressig, F.; Zanusso, O., J. High Energy Phys., 08, 113, (2015) · Zbl 1388.83105 |
| [66] | Ohta, N.; Percacci, R.; Vacca, G. P., Eur. Phys. J. C, 76, 46, (2016) |
| [67] | Labus, P.; Morris, T. R.; Slade, Z. H., Phys. Rev. D, 94, (2016) |
| [68] | Dietz, J. A.; Morris, T. R.; Slade, Z. H., Phys. Rev. D, 94, (2016) |
| [69] | N. Christiansen, K. Falls, J.M. Pawlowski, M. Reichert, arXiv:1711.09259; N. Christiansen, K. Falls, J.M. Pawlowski, M. Reichert, arXiv:1711.09259 |
| [70] | B. Knorr, arXiv:1710.07055; B. Knorr, arXiv:1710.07055 |
| [71] | K.G. Falls, C.S. King, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1801.00162; K.G. Falls, C.S. King, D.F. Litim, K. Nikolakopoulos, C. Rahmede, arXiv:1801.00162 |
| [72] | Gies, H.; Knorr, B.; Lippoldt, S.; Saueressig, F., Phys. Rev. Lett., 116, (2016) |
| [73] | Manrique, E.; Rechenberger, S.; Saueressig, F., Phys. Rev. Lett., 106, (2011) |
| [74] | Rechenberger, S.; Saueressig, F., J. High Energy Phys., 03, 010, (2013) |
| [75] | Biemans, J.; Platania, A.; Saueressig, F., Phys. Rev. D, 95, (2017) |
| [76] | Biemans, J.; Platania, A.; Saueressig, F., J. High Energy Phys., 05, 093, (2017) · Zbl 1380.83088 |
| [77] | Houthoff, W. B.; Kurov, A.; Saueressig, F., Eur. Phys. J. C, 77, 491, (2017) |
| [78] | Dou, D.; Percacci, R., Classical Quantum Gravity, 15, 3449, (1998), hep-th/9707239 |
| [79] | Percacci, R.; Perini, D., Phys. Rev. D, 67, (2003), hep-th/0207033 |
| [80] | Narain, G.; Percacci, R., Classical Quantum Gravity, 27, (2010) |
| [81] | Daum, J.-E.; Harst, U.; Reuter, M., Gen. Relativity Gravitation, 43, 2393, (2011) · Zbl 1225.83030 |
| [82] | Folkerts, S.; Litim, D. F.; Pawlowski, J. M., Phys. Lett. B, 709, 234, (2012) |
| [83] | Harst, U.; Reuter, M., J. High Energy Phys., 05, 119, (2011) · Zbl 1296.83026 |
| [84] | Eichhorn, A.; Gies, H., New J. Phys., 13, (2011) |
| [85] | Eichhorn, A., Phys. Rev. D, 86, (2012) |
| [86] | Donà, P.; Percacci, R., Phys. Rev. D, 87, (2013) |
| [87] | Henz, T.; Pawlowski, J. M.; Rodigast, A.; Wetterich, C., Phys. Lett. B, 727, 298, (2013) · Zbl 1331.81216 |
| [88] | Donà, P.; Eichhorn, A.; Percacci, R., Phys. Rev. D, 89, (2014) |
| [89] | Percacci, R.; Vacca, G. P., Eur. Phys. J. C, 75, 188, (2015) |
| [90] | Labus, P.; Percacci, R.; Vacca, G. P., Phys. Lett. B, 753, 274, (2016) · Zbl 1367.83074 |
| [91] | Oda, K.y.; Yamada, M., Classical Quantum Gravity, 33, (2016) |
| [92] | Meibohm, J.; Pawlowski, J. M.; Reichert, M., Phys. Rev. D, 93, (2016) |
| [93] | Donà, P.; Eichhorn, A.; Labus, P.; Percacci, R., Phys. Rev. D, Phys. Rev. D, 93, 12, 129904, (2016), Erratum |
| [94] | Meibohm, J.; Pawlowski, J. M., Eur. Phys. J. C, 76, 285, (2016) |
| [95] | Eichhorn, A.; Held, A.; Pawlowski, J. M., Phys. Rev. D, 94, (2016) |
| [96] | Henz, T.; Pawlowski, J. M.; Wetterich, C., Phys. Lett. B, 769, 105, (2017) · Zbl 1370.81199 |
| [97] | Eichhorn, A.; Lippoldt, S., Phys. Lett. B, 767, 142, (2017) |
| [98] | Christiansen, N.; Eichhorn, A., Phys. Lett. B, 770, 154, (2017) · Zbl 1403.81063 |
| [99] | Eichhorn, A.; Held, A., Phys. Rev. D, 96, (2017) |
| [100] | Christiansen, N.; Eichhorn, A.; Held, A., Phys. Rev. D, 96, (2017) |
| [101] | Eichhorn, A.; Held, A., Phys. Lett. B, 777, 217, (2018) |
| [102] | Eichhorn, A.; Versteegen, F., J. High Energy Phys., 01, 030, (2018) · Zbl 1384.83015 |
| [103] | A. Eichhorn, arXiv:1709.03696; A. Eichhorn, arXiv:1709.03696 |
| [104] | N. Christiansen, D.F. Litim, J.M. Pawlowski, M. Reichert, arXiv:1710.04669; N. Christiansen, D.F. Litim, J.M. Pawlowski, M. Reichert, arXiv:1710.04669 |
| [105] | J. Schröder, Aspects of Quantum Gravity and Matter, (Doctoral dissertation), retrieved via Sussex Research Online.; J. Schröder, Aspects of Quantum Gravity and Matter, (Doctoral dissertation), retrieved via Sussex Research Online. |
| [106] | Wetterich, C., Phys. Lett. B, 301, 90, (1993) |
| [107] | Morris, T. R., Internat. J. Modern Phys. A, 9, 2411, (1994), hep-ph/9308265 |
| [108] | Rubin, M. A.; Ordonez, C. R., J. Math. Phys., J. Math. Phys., 26, 65, (1985) · Zbl 0554.58050 |
| [109] | Camporesi, R.; Higuchi, A., J. Geom. Phys., 20, 1, (1996), gr-qc/9505009 |
| [110] | York, J. W., J. Math. Phys., 14, 456, (1973) · Zbl 0259.53014 |
| [111] | Benedetti, D., New J. Phys., 14, (2012) |
| [112] | F. Saueressig, A. Vereijken, in preparation.; F. Saueressig, A. Vereijken, in preparation. |
| [113] | Litim, D. F., Phys. Lett. B, 486, 92, (2000), [hep-th/0005245] |
| [114] | Litim, D. F., Phys. Rev. D, 64, (2001), [hep-th/0103195] |
| [115] | N. Alkofer, F. Saueressig, in preparation.; N. Alkofer, F. Saueressig, in preparation. |
| [116] | Wetterich, C., Phys. Lett. B, 773, 6, (2017) · Zbl 1378.83025 |
| [117] | Reuter, M.; Saueressig, F., Quantum gravity and the functional renormalization group - the road towards asymptotic safety, (2018), Camb. Univ. Press, (in press) · Zbl 1434.83006 |
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