Abstract
We generalize the local renormalization group (RG) equation to theories with chiral anomalies. We find that a new anomaly is required by the Wess-Zumino consistency conditions. Taking into account the new anomaly, the trace of the energy momentum tensor is expressed in terms of the covariant flavor currents, instead of the consistent ones. This result is used to show that a flavor rotation induced by the RG flow can be eliminated by a choice of scheme even in the presence of chiral anomalies. As part of a general discussion of chiral anomalies in the presence of background sources, we also derive non-renormalization theorems. Finally, we introduce the θ parameter as a source, and derive constraints on a perturbative running of this parameter.
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References
I.T. Drummond and G.M. Shore, Conformal Anomalies for Interacting Scalar Fields in Curved Space-Time, Phys. Rev. D 19 (1979) 1134 [INSPIRE].
H. Osborn, Weyl consistency conditions and a local renormalization group equation for general renormalizable field theories, Nucl. Phys. B 363 (1991) 486 [INSPIRE].
I. Jack and H. Osborn, Constraints on RG Flow for Four Dimensional Quantum Field Theories, Nucl. Phys. B 883 (2014) 425 [arXiv:1312.0428] [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
M.A. Luty, J. Polchinski and R. Rattazzi, The a-theorem and the Asymptotics of 4D Quantum Field Theory, JHEP 01 (2013) 152 [arXiv:1204.5221] [INSPIRE].
F. Baume, B. Keren-Zur, R. Rattazzi and L. Vitale, The local Callan-Symanzik equation: structure and applications, arXiv:1401.5983 [INSPIRE].
J.-F. Fortin, B. Grinstein and A. Stergiou, Limit Cycles and Conformal Invariance, JHEP 01 (2013) 184 [arXiv:1208.3674] [INSPIRE].
S.L. Adler and W.A. Bardeen, Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev. 182 (1969) 1517 [INSPIRE].
W.A. Bardeen and B. Zumino, Consistent and Covariant Anomalies in Gauge and Gravitational Theories, Nucl. Phys. B 244 (1984) 421 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Univeristy Press, Cambridge, U.K. (1996).
L. Bonora, P. Pasti and M. Bregola, Weyl Cocycles, Class. Quant. Grav. 3 (1986) 635 [INSPIRE].
Y. Nakayama, CP-violating CFT and trace anomaly, Nucl. Phys. B 859 (2012) 288 [arXiv:1201.3428] [INSPIRE].
Y. Nakayama, Vector β-function, Int. J. Mod. Phys. A 28 (2013) 1350166 [arXiv:1310.0574] [INSPIRE].
A. Zee, Axial vector anomalies and the scaling property of field theory, Phys. Rev. Lett. 29 (1972) 1198 [INSPIRE].
S.A. Larin, The Renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
J.R. Ellis and M.K. Gaillard, Strong and Weak CP-violation, Nucl. Phys. B 150 (1979) 141 [INSPIRE].
A.E. Nelson, Naturally Weak CP-violation, Phys. Lett. B 136 (1984) 387 [INSPIRE].
H. Osborn, Local couplings and SL(2, ℝ) invariance for gauge theories at one loop, Phys. Lett. B 561 (2003) 174 [hep-th/0302119] [INSPIRE].
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ArXiv ePrint: 1406.0869
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Keren-Zur, B. The local RG equation and chiral anomalies. J. High Energ. Phys. 2014, 11 (2014). https://doi.org/10.1007/JHEP09(2014)011
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DOI: https://doi.org/10.1007/JHEP09(2014)011