Quantum Gravitational Contributions to Gauge Field Theories

TANG Yong; WU Yue-Liang

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Communications in Theoretical Physics ›› 2012, Vol. 57 ›› Issue (4) : 629-636.

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Quantum Gravitational Contributions to Gauge Field Theories

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Abstract

We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky-DeWitt formalism based on the background field method. With the advantage of Landau-DeWitt gauge, we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings. By employing, in a general way, a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals, we show that the resulting gauge coupling is power-law running and asymptotically free. The regularization scheme dependence is clarified by comparing with results obtained by other methods. The loop regularization scheme is found to be applicable for a consistent calculation.

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quantum gravity / Vilkovisky-DeWitt / asymptotic freedom

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TANG Yong, WU Yue-Liang. Quantum Gravitational Contributions to Gauge Field Theories[J]. Communications in Theoretical Physics, 2012, 57(4): 629-636

References

[1] S.P.Robinson and F.Wilczek,Phys.Rev.Lett.96 (2006) 231601.
[2] A.R.Pietrykowski,Phys.Rev.Lett.98 (2007) 061801.
[3] D.J.Toms,Phys.Rev.D 76 (2007) 045015.
[4] G.A.Vilkovisky,Nucl.Phys.B 234 (1984) 125,The Quantum Theory of Gravity/ ed. S.M.Christensen,Adam Hilger,Bristo (1984).
[5] B.S.DeWitt,in Quantum Field Theory and Quantum Statistics,Volume 1,eds. I.A.Batalin,C.J.Isham,and G.A.Vilkovisky,Adam Hilger,Bristol (1987).
[6] G.'t Hooft and M.Veltman,Nucl.Phys.B 44 (1972) 189.
[7] D.Ebert,J.Plefka,and A.Rodigast,Phys.Lett.B 660 (2008) 579.
[8] Y.L.Wu,Int.J.Mod.Phys.A 18 (2003) 5363,[arXiv:hep-th/0209021]; Mod.Phys.Lett.A 19 (2004) 2191,[arXiv:hep-th/0311082].
[9] Y.Tang and Y.L.Wu,Commun.Theor.Phys.54 (2010) 1040,arXiv:0807.0331v2 [hep-ph].
[10] J.E.Daum,U.Harst,and M.Reuter,J.High Energy Phys.1001 (2001) 084.
[11] F.Wu and M.Zhong,Phys.Lett.B 659 (2008) 694,Phys.Rev.D 78 (2008) 085010.
[12] A.Rodigast and T.Schuster,Phys.Rev.D 79 (2009) 125017,Phys.Rev.Lett.104 (2010) 081301.
[13] O.Zanusso,L.Zambelli,G.P.Vacca,and R.Percacci,Phys.Lett.B 689 (2010) 90.
[14] P.T.Mackay and D.J.Toms,Phys.Lett.B 684 (2010) 251.
[15] M.M.Anber,J.F.Donoghue,and M.El-Houssieny,arXiv: 1011.3229 [ hep-th].
[16] J.Ellis and N.E.Mavromatos,arXiv:1012:4353 [hep-th].
[17] D.J.Toms,Nature (London) 468 (2010) 56.
[18] H.J.He,X.F.Wang,and Z.Z.Xianyu,arXiv:1008.1839 [hep-th].
[19] Note that the field metric g_ij used by two groups differ by a factor of 2,and also different regularization schemes are adopted by two groups.
[20] Y.B.Dai and Y.L.Wu,Eur.Phys.J.C 39 (2004) S1 [arXiv:hep-ph/0304075]; J.W.Cui and Y.L.Wu,Int.J.Mod. Phys.A 23 (2008) 2861,[arXiv:0801.2199 [hep-ph]; J.W.Cui,Y.Tang,and Y.L.Wu,Phys. Rev. D 79 (2009) 125008,[arXiv:0812.0892 [hep-ph]; Y.L.Ma and Y.L.Wu,Int.J.Mod.Phys.A 21 (2006) 6383,[arXiv:hep-ph/0509083]; Y.L.Ma and Y.L.Wu,Phys.Lett.B 647 (2007) 427,[arXiv:hep-ph/0611199]; J.W.Cui,Y.L.Ma,and Y.L.Wu,Phys.Rev.D 84 (2011) 025020,arXiv:1103.2026 [hep-ph].
[21] D.Huang and Y.L.Wu,e-Print: arXiv:1108.3603 [hep-ph].
[22] D.J.Toms,Phys.Rev.Lett.101 (2008) 131301,Phys.Rev.D 80 (2009) 064040.
[23] L.Parker and D.J.Toms,Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity/,Cambridge University Press,Cambridge (2009).
[24] B.S.DeWitt,The Dynamical Theory of Groups and Fields/,Gordon and Breach,New York (1965).
[25] L.D.Faddeev and V.N.Popov,Phys.Lett.B 25 (1967) 29.
[26] There is in general a freedom in the choice of field metric g_ij ,a discussion on the dependence of g_ij may also be found in S.D.Odintsov,Phys.Lett.B 262 (1991) 394.However,when imposing the requirements on the choice of g_ij given in Refs.[4,29] the field metric g_ij becomes unique and it was actually used in Ref.
[17].In our present calculations,we will use such a convention.
[27] Y.Tang and Y.L.Wu,J.High Energy Phys.1111 (2011) 073,arXiv:1109.4001 [hep-ph].
[28] E.S.Fradkin and A.A.Tseytlin,Nucl.Phys.B 234 (1984) 509.
[29] A.O.Barvinsky and G.A.Vilkovisky,Phys.Reports 119 (1985) 1.
[30] S.R.Huggins,G.Kunstatter,H.P.Leivo,and D.J.Toms,Nucl.Phys.B 301 (1987) 627.
[31] R.Mertig,M.Böhm,and A.Denner,Comput.Phys.Commun.64 (1991) 345.
[32] See e.g.: T.P.Cheng and L.F.Li,Gauge Theory of Elementary Particle Physics,Oxford University Press,Oxford OX2 6DP (1984); reprinted 1985-1996; Y.B.Dai,Gauge Theory of Interactions,Scientific Publishing,Beijing (1987); M.E.Peskin and D.V.Schroeder,An Introduction to Quantum Field Theory,Westview Press,Colorado (1995).
[33] S.Folkerts,D.F.Litim,and J.M.Pawlowski,e-print: arXiv:1101.5552 [hep-th].
[34] J.C.C.Felipe,L.C.T.Brito,M.Sampaio,and M.C.Nemes,Phys.Lett.B 700 (2011) 86.

Funding

Supported in part by the National Science Foundation of China under Grant Nos.10821504,10975170,and the Key Project of Knowledge Innovation Program of Chinese Academy of Science