Remarks on Two-Dimensional Power Correction in Soft Wall Model
HUANG Tao, ZUO Fen
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 1000492Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049
Remarks on Two-Dimensional Power Correction in Soft Wall Model
HUANG Tao, ZUO Fen
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 1000492Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049
摘要We present a direct derivation of the two-point correlation function of the vector current in the soft wall model by using the AdS/CFT dictionary. The resulting correlator is exactly the same as the one previously obtained from dispersion relation with the same spectral function as in this model. The coefficient C2 of the two-dimensional power correction is found to be C2=-c/2 with c the slope of the Regge trajectory, rather than C2=-c/3 derived from the strategy of the first quantized string theory. Taking the slope of the ρ trajectory c≈0.9GeV2 as input, we then obtain C2≈-0.45GeV2. The gluon condensate is found to be <αsG2>≈pprox0.064GeV4, which is almost identical to the QCD sum rule estimation. By comparing these two equivalent derivation of the correlator of scalar glueball operator, we demonstrate that the two-dimensional correction cannot be eliminated by including the non-leading solution in the bulk-to-boundary propagator, as carried out by Colangelo et al.[arXiv:0711.4747]. In other words, the two-dimensional correction does exist in the scalar glueball case. Also it is manifest by using the dispersion relation that the minus sign of gluon condensate and violation of the low energy theorem are related to the subtraction scheme.
Abstract：We present a direct derivation of the two-point correlation function of the vector current in the soft wall model by using the AdS/CFT dictionary. The resulting correlator is exactly the same as the one previously obtained from dispersion relation with the same spectral function as in this model. The coefficient C2 of the two-dimensional power correction is found to be C2=-c/2 with c the slope of the Regge trajectory, rather than C2=-c/3 derived from the strategy of the first quantized string theory. Taking the slope of the ρ trajectory c≈0.9GeV2 as input, we then obtain C2≈-0.45GeV2. The gluon condensate is found to be <αsG2>≈pprox0.064GeV4, which is almost identical to the QCD sum rule estimation. By comparing these two equivalent derivation of the correlator of scalar glueball operator, we demonstrate that the two-dimensional correction cannot be eliminated by including the non-leading solution in the bulk-to-boundary propagator, as carried out by Colangelo et al.[arXiv:0711.4747]. In other words, the two-dimensional correction does exist in the scalar glueball case. Also it is manifest by using the dispersion relation that the minus sign of gluon condensate and violation of the low energy theorem are related to the subtraction scheme.
[1] Shifman M A, Vainshtein A I and Zakharov V I 1979 Nucl. Phys. B147 385 [2]Zakharov V I 1998 Prog. Theor. Phys. Suppl. 131107 [3]Dorokhov A E and Broniowski W 2003 Eur. Phys. J. C 32 79 [4]Shifman M arXiv: hep-ph/0009131 [5]Arriola E R and Broniowski W 2006 Phys. Rev. D 73 097502 [6]Andreev O 2006 Phys. Rev. D 73 107901 [7]Karch A, Katz E, Son D T, and Stephanov M A 2006 Phys.Rev. D 74 015005 [8]Maldacena J M 1998 Adv. Theor. Math. Phys. 2231 [9]Cat\`{a O 2007 Phys. Rev. D 75 106004 [10]Narison S 1989 World Scientific Notes in Physics vol26 [11]Forkel H arXiv: 0711.1179 [12]Colangelo P, De Fazio F, Jugeau F and Nicotri S arXiv:0711.4747 [13]Hoon S, Yoon S and Strassler M 2006 J. High EnergyPhys. 04 003 [14]Grigoryan H R and Radyushkin A V 2007 Phys. Rev. D 76 095007 [15] Gubser S S, Klebanov I R and Polyakov A M 1998 Phys.Lett. B 428 105 [16]Witten E 1998 Adv. Theor. Math. Phys. 2 253 [17]Erd\'{elyi A 1953 Higher Transcendental Functions(New York: McGRAW-HILL) vol I % [18]Cat\`{a O, Golterman M and Peris S 2005 J. High%Energy Phys. 08 076 [19]Erlich J, Katz E, Son D T, and Stephanov M A 2005 Phys. Rev. Lett. 95 261602 [20]Colangelo P, De Fazio F, Jugeau F and Nicotri S 2007 Phys. Lett. B 652 73 % [21]Wang Z X and Guo D R 1989 Special Functions%(Singapore: World Scientific)
2008, Vol. 25 
