Abstract
The anomaly implies an obstruction to a fully chiral covariant calculation of the effective action in the abnormal-parity sector of chiral theories. The standard approach then is to reconstruct the anomalous effective action from its covariant current. In this work, we use a recently introduced formulation which allows one to directly construct the non-trivial chiral invariant part of the effective action within a fully covariant formalism. To this end we develop an appropriate version of Chan’s approach to carry out the calculation within the derivative expansion. The result to four derivatives, i.e., to leading order in two and four dimensions and next-to-leading order in two dimensions, is explicitly worked out. Fairly compact expressions are found for these terms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Itzykson, J.B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980)
K. Fujikawa, Phys. Rev. Lett. 42, 1195 (1979)
S.L. Adler, Phys. Rev. 177, 2426 (1969)
J.S. Bell, R. Jackiw, Nuovo Cim. A 60, 47 (1969)
W.A. Bardeen, Phys. Rev. 184, 1848 (1969)
L. Álvarez-Gaumé, E. Witten, Nucl. Phys. B 234, 269 (1984)
S.L. Adler, W.A. Bardeen, Phys. Rev. 182, 1517 (1969)
J. Wess, B. Zumino, Phys. Lett. B 37, 95 (1971)
J. Goldstone, F. Wilczek, Phys. Rev. Lett. 47, 986 (1981)
E. Witten, Nucl. Phys. B 223, 422 (1983)
W.A. Bardeen, B. Zumino, Nucl. Phys. B 244, 421 (1984)
E. D’Hoker, E. Farhi, Nucl. Phys. B 248, 59 (1984)
H. Leutwyler, Phys. Lett. B 152, 78 (1985)
L. Álvarez-Gaumé, P. Ginsparg, Ann. Phys. 161, 423 (1985)
H. Banerjee, R. Banerjee, P. Mitra, Z. Phys. C 32, 445 (1986)
R.D. Ball, Phys. Rep. 182, 1 (1989)
L.L. Salcedo, Eur. Phys. J. C 20, 161 (2001). hep-th/0012174
A. Hernández, T. Konstandin, M.G. Schmidt, Nucl. Phys. B 793, 425 (2008). arXiv:0708.0759 [hep-th]
L.L. Salcedo, Eur. Phys. J. C 58, 423 (2008). arxiv:0807.1696
A. Hernandez, T. Konstandin, M.G. Schmidt, Nucl. Phys. B. 812, 290 (2009). arXiv:0810.4092 [hep-ph]
L.H. Chan, Phys. Rev. Lett. 57, 1199 (1986)
J. Smit, J. High Energy Phys. 09, 067 (2004). hep-ph/0407161
L.L. Salcedo, Eur. Phys. J. C 20, 147 (2001). hep-th/0012166
A. Dhar, R. Shankar, S.R. Wadia, Phys. Rev. D 31, 3256 (1985)
L.L. Salcedo, E. Ruiz Arriola, Ann. Phys. 250, 1 (1996). hep-th/9412140
S.W. Hawking, Commun. Math. Phys. 55, 133 (1977)
E. Elizalde , Zeta Regularization Techniques with Applications (World Scientific, Singapore, 1994)
R.P. Feynman, Phys. Rev. 84, 108 (1951)
C. García-Recio, L.L. Salcedo, Phys. Rev. D 63, 045016 (2001). hep-th/0007183
L.L. Salcedo, Eur. Phys. J. C 37, 511 (2004). hep-th/0409140
M. Nakahara, Geometry, Topology and Physics. Graduate Student Series in Physics (IOP, Bristol, 1990)
R.A. Bertlmann, Anomalies in Quantum Field Theory (Oxford University Press, Oxford, 1996)
N.G. Pletnev, A.T. Banin, Phys. Rev. D 60, 105017 (1999). hep-th/9811031
L.L. Salcedo, Eur. Phys. J. C 49, 831 (2007). hep-th/0606071
J. Caro, L.L. Salcedo, Phys. Lett. B 309, 359 (1993)
L.L. Salcedo, Phys. Rev. D 76, 044009 (2007). arXiv:0706.1875 [hep-th]
M.J. Strassler, Nucl. Phys. B 385, 145 (1992). hep-ph/9205205
M.G. Schmidt, C. Schubert, Phys. Lett. B 318, 438 (1993). hep-th/9309055
L.L. Salcedo, Phys. Rev. D 58, 125007 (1998). hep-th/9807221
A. Gómez Nicola, R.F. Álvarez-Estrada, Int. J. Mod. Phys. A 9, 1423 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Salcedo, L.L. Direct construction of the effective action of chiral gauge fermions in the anomalous sector. Eur. Phys. J. C 60, 387–402 (2009). https://doi.org/10.1140/epjc/s10052-009-0923-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-009-0923-4