Standard model gauging of the Wess-Zumino-Witten term: Anomalies, global currents, and pseudo-Chern-Simons interactions

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 77, Issue 8, 2008, Pages

  Harvey, Jeffrey A ^a   Hill, Christopher T ^b   Hill, Richard J ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b FERMI NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42449154649     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.77.085017     Document Type: Article

References (35)

1. J. Wess and B. Zumino, Phys. Lett. B 37, 95 (1971). PYLBAJ 0370-2693 10.1016/0370-2693(71)90582-X
2. E. Witten, Nucl. Phys. NUPBBO 0550-3213 B223, 422 (1983). 10.1016/0550-3213(83)90063-9
3. J. Steinberger, Phys. Rev. 76, 1180 (1949). PHRVAO 0031-899X 10.1103/PhysRev.76.1180
4. J.S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969). NCIAAT 0369-3546
5. S.L. Adler, Phys. Rev. 177, 2426 (1969). PHRVAO 0031-899X 10.1103/PhysRev.177.2426
6. W.A. Bardeen, Phys. Rev. 184, 1848 (1969). PHRVAO 0031-899X 10.1103/PhysRev.184.1848
7. O. Kaymakcalan, S. Rajeev, and J. Schechter, Phys. Rev. D 30, 594 (1984). PRVDAQ 0556-2821 10.1103/PhysRevD.30.594
8. A. Manohar and G.W. Moore, Nucl. Phys. NUPBBO 0550-3213 B243, 55 (1984). 10.1016/0550-3213(84)90385-7
9. H. Kawai and S.H.H. Tye, Phys. Lett. B 140, 403 (1984). PYLBAJ 0370-2693 10.1016/0370-2693(84)90780-9
10. C.T. Hill and R.J. Hill, Phys. Rev. D 76, 115014 (2007); PRVDAQ 0556-2821 10.1103/PhysRevD.76.115014
11. C.T. Hill R.J. Hill Phys. Rev. D 75, 115009 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.115009
12. J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47, 986 (1981). PRLTAO 0031-9007 10.1103/PhysRevLett.47.986
13. Weyl spinor triangle loops yield a finite and unambiguous form of the anomaly that satisfies the Wess-Zumino consistency condition, hence known as the consistent anomaly. Dirac fermions have ambiguities arising from the left-right mixing via the mass term. Bardeen obtains the consistent anomaly for massive Dirac fermions by imposing the left-right symmetry of the classical Dirac action on the result. The counterterm can be viewed as a definition of the fermion loop. Throughout this paper we will always assume that the fermion loops explicitly generate the consistent anomaly, and that the counterterm is appended to the action, since this is the appropriate implementation for the Wess-Zumino-Witten term. The counterterm in the action can be seen as arising from a Chern-Simons term in a D=5 theory with chiral delocalization of fermions on boundary branes, compactifying the theory to D=4.
14. In the case of QED, the covariant anomaly is distinguished from the consistent anomaly only by the factor of 3 in its coefficient. In a Yang-Mills theory the consistent anomaly is not gauge covariant, while the covariant anomaly is.
15. Interactions of this form are often referred to as "Chern- Simons" terms, though technically this is a misnomer. Chern-Simons terms occur only in odd dimensions and generate anomalies on boundaries. In even D we refer to terms like V(1)V(2)dV(3) as pseudo-Chern-Simons terms (or pCS terms) which generate anomalies in the bulk.
16. See the review of M. Harada and K. Yamawaki, Phys. Rep. 381, 1 (2003), and references therein. PRPLCM 0370-1573 10.1016/S0370-1573(03)00139-X
17. J.A. Harvey, C.T. Hill, and R.J. Hill (work in progress).
18. J.A. Harvey, C.T. Hill, and R.J. Hill, Phys. Rev. Lett. 99, 261601 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.261601
19. A.A. Aguilar-Arevalo (MiniBooNE Collaboration), Phys. Rev. Lett. 98, 231801 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.231801
20. N. Kaiser and U.G. Meissner, Nucl. Phys. A 519, 671 (1990). NUPABL 0375-9474 10.1016/0375-9474(90)90431-K
21. F. Klingl, N. Kaiser, and W. Weise, Z. Phys. A ZPAHEX 0939-7922 356, 193 (1996).
22. E. Truhlik, J. Smejkal, and F.C. Khanna, Nucl. Phys. A 689, 741 (2001). NUPABL 0375-9474 10.1016/S0375-9474(00)00610-2
23. E. D'Hoker and E. Farhi, Nucl. Phys. NUPBBO 0550-3213 B248, 59 (1984). 10.1016/0550-3213(84)90586-8
24. E. D'Hoker and E. Farhi, Nucl. Phys. NUPBBO 0550-3213 B248, 77 (1984). 10.1016/0550-3213(84)90587-X
25. C.T. Hill and C.K. Zachos, Phys. Rev. D 71, 046002 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.71.046002
26. C.T. Hill, Phys. Rev. D 73, 126009 (2006); PRVDAQ 0556-2821 10.1103/PhysRevD.73.126009
27. C.T. Hill Phys. Rev. D 73, 085001 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.085001
28. C.T. Hill and C.K. Zachos, arXiv:0802.1672.
29. S.R. Coleman, J. Wess, and B. Zumino, Phys. Rev. 177, 2239 (1969); PHRVAO 0031-899X 10.1103/PhysRev.177.2239
30. C.G. Callan, S.R. Coleman, J. Wess, and B. Zumino, Phys. Rev. 177, 2247 (1969). PHRVAO 0031-899X 10.1103/PhysRev.177.2247
31. C.S. Chu, P.M. Ho, and B. Zumino, Nucl. Phys. NUPBBO 0550-3213 B475, 484 (1996). 10.1016/0550-3213(96)00322-7
32. C.G. Callan and E. Witten, Nucl. Phys. NUPBBO 0550-3213 B239, 161 (1984). 10.1016/0550-3213(84)90088-9
33. C.T. Hill, Phys. Rev. Lett. 88, 041601 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.88.041601
34. R.J. Hill (work in progress).
35. S.K. Domokos and J.A. Harvey, Phys. Rev. Lett. 99, 141602 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.141602