Research PapersNo Access

Analysis of an $S U (8)$ model with a spin- $\frac{1}{2}$ field directly coupled to a gauged Rarita–Schwinger spin- $\frac{3}{2}$ field

Stephen L. Adler

Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA

https://doi.org/10.1142/S0217751X19502300Cited by:3 (Source: Crossref)

Abstract

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin- $\frac{3}{2}$ field is directly coupled to a spin- $\frac{1}{2}$ field. Here, we extend this analysis to the gauged $S U (8)$ model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation $\bar{8}$ spin- $\frac{1}{2}$ fermion to the original fermion complement of the $S U (8)$ model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated $S U (8)$ model, including a possible connection to the $E_{8}$ root lattice.

Keywords:

PACS: 12.10.Dm, 12.60.Cn

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. S. L. Adler, Phys. Rev. D 97, 045014 (2018). Web of Science, ADS, Google Scholar
2. S. L. Adler, M. Henneaux and P. Pais, Phys. Rev. D 96, 085005 (2017). Web of Science, ADS, Google Scholar
3. S. L. Adler and P. Pais, Phys. Rev. D 99, 095037 (2019). Web of Science, ADS, Google Scholar
4. M. J. Duff, Ultraviolet divergences in extended supergravity, in Supergravity ’81, eds. S. Ferrara and J. G. Taylor (Cambridge University Press, Cambridge, 1982), p. 197 (also S. Ferrara and J. G. Taylor, CERN TH. 3232, p. 41). Google Scholar
5. L. Alvarez-Gaumé and E. Witten, Nucl. Phys. B 234, 269 (1984). Web of Science, ADS, Google Scholar
6. N. K. Nielsen and H. Römer, Phys. Lett. B 154, 141 (1985). Web of Science, ADS, Google Scholar
7. S. M. Christensen and M. J. Duff, Phys. Lett. B 76, 571 (1978). Web of Science, ADS, Google Scholar
8. S. M. Christensen and M. J. Duff, Nucl. Phys. B 154, 301 (1979). Web of Science, ADS, Google Scholar
9. N. K. Nielsen, Nucl. Phys. B 140, 499 (1978). Web of Science, ADS, Google Scholar
10. N. K. Nielsen, M. T. Grisaru, H. Römer and P. Van Nieuwenhuizen, Nucl. Phys. B 140, 477 (1978). Web of Science, ADS, Google Scholar
11. N. Marcus, Phys. Lett. B 157, 383 (1985). Web of Science, ADS, Google Scholar
12. S. L. Adler, Int. J. Mod. Phys. A 29, 1450130 (2014). Link, Web of Science, ADS, Google Scholar
13. S. L. Adler, J. Phys. A: Math Theor. 49, 315401 (2016). Web of Science, ADS, Google Scholar
14. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973). Web of Science, ADS, Google Scholar
15. T. L. Curtright and P. G. O. Freund, $S U (8)$ unification and supergravity, in Supergravity, eds. P. van Nieuwenhuizen and D. Z. Freedman (North-Holland, 1979), pp. 197–201. Google Scholar
16. C. W. Kim and C. Roiesnel, Phys. Lett. B 93, 343 (1980). Web of Science, ADS, Google Scholar
17. J. Chakrabarti, M. Popović and R. N. Mohapatra, Phys. Rev. D 21, 3212 (1980). Web of Science, ADS, Google Scholar
18. J. E. Kim and H. S. Song, Phys. Rev. D 25, 2996 (1982). Web of Science, ADS, Google Scholar
19. S. K. Yun, Phys. Rev. D 29, 1494 (1984). Web of Science, ADS, Google Scholar
20. S. L. Adler, J. Phys. A: Math Theor. 50, 295401 (2017). Web of Science, ADS, Google Scholar
21. R. Slansky, Phys. Rep. 79, 1, 34–35, 114 (1981). Web of Science, ADS, Google Scholar
22. W. G. McKay and J. Patera, Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras (Marcel Dekker, New York and Basel, 1981). Google Scholar
23. S. Weinberg, Phys. Rev. Lett. 29, 388 (1972). Web of Science, ADS, Google Scholar
24. Wikipedia, $E_{8}$ lattice, http://en.wikipedia.org/wiki/E8_lattice. Google Scholar
25. Wikipedia, $E_{8}$ (mathematics), http://en.wikipedia.org/wiki/E8_(mathematics). Google Scholar
26. D. Madore, The $E_{8}$ root system, http://www.madore.org/~david/math/e8w.html. Google Scholar