Prog. Theor. Phys. Vol. 91 No. 4 (1994) pp. 801-828
Low Energy Theorems of Hidden Local Symmetries
Department of Physics, Kyoto University, Kyoto 606-01
*Department of Physics, Nagoya University, Nagoya 464-01
(Received December 17, 1993)
We prove to all orders of the loop expansion the low energy theorems of hidden local symmetries in four-dimensional nonlinear sigma models based on the coset space G/H, with G and H being arbitrary compact groups. Although the models are non-renormalizable, the proof is done in an analogous manner to the renormalization proof of gauge theories and two-dimensional nonlinear sigma models by restricting ourselves to the operators with two derivatives (counting a hidden gauge boson field as one derivative), i.e., with dimension 2, which are the only operators relevant to the low energy limit. Through loop-wise mathematical induction based on the Ward-Takahashi identity for the BRS symmetry, we solve renormalization equation for the effective action up to dimension-2 terms plus terms with the relevant BRS sources. We then show that all the quantum corrections to the dimension-2 operators, including the finite parts as well as the divergent ones, can be entirely absorbed into a re-definition (renormalization) of the parameters and the fields in the dimension-2 part of the tree-level Lagrangian.
DOI : 10.1143/PTP.91.801
M. Bando, T. Kugo and K. Yamawaki, Phys. Rep. 164 (1988), 217[CrossRef].
M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, Phys. Rev. Lett. 54 (1985), 1215[APS].
- J. J. Sakurai, Currents and Mesons (Chicago Univ. Press, Chicago, 1969).
K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16 (1966), 255[APS].
Riazuddin and Fayyazuddin, Phys. Rev. 147 (1966), 1071[APS].
- M. Bando, T. Kugo and K. Yamawaki, Nucl. Phys. B259 (1985), 493.
- M. Bando, T. Kugo and K. Yamawaki, Prog. Theor. Phys. 73 (1985), 1541[PTP].
- M. Harada and K. Yamawaki, Phys. Lett. B297 (1992), 151.
M. Harada, T. Kugo and K. Yamawaki, Phys. Rev. Lett. 71 (1993), 1299[APS].
C. Becchi, A. Rouet and R. Stora, Ann. of Phys. 98 (1976), 287[CrossRef].
- J. Zinn-Justin, “Renormalization of Gauge Theories" in Lecture Notes in Physics 37 (Springer, 1975).
B. W. Lee, “Gauge Theories" in Methods in Field Theory, Les Houches, 1975 (North-Holland, 1976).
- A. Blasi and R. Collina, Nucl. Phys. B258 (1987), 204; Phys. Lett. B200 (1988), 98.
C. Becchi, A. Blasi, G. Bonneau, R. Collina and F. Delduc, Commun. Math. Phys. 120 (1988), 121[CrossRef].
- S. Weinberg, Physica 96A (1979), 327.
T. Appelquist and C. Bernard, Phys. Rev. D23 (1981), 425[APS].
J. Gasser and H. Leutwyler, Ann. of Phys. 158 (1984), 142[CrossRef].
C. G. Callan, S. Coleman, J. Wess and B. Zumino, Phys. Rev. 177 (1969), 2247[APS].
M. Boulware and L. S. Brown, Ann. of Phys. 138 (1982), 392[CrossRef].
- N. Nakanishi, Prog. Theor. Phys. 51 (1974), 952[PTP].
- T. Fujiwara, T. Kugo, H. Terao, S. Uehara and K. Yamawaki, Prog. Theor. Phys. 73 (1985), 926[PTP].
H. Georgi, Phys. Rev. Lett. 63 (1989), 1917[APS]; Nucl. Phys. B331 (1990), 311.
S. Weinberg, Phys. Rev. 166 (1968), 1568[APS].