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A connection between grand unified theories and extended supergravities

Связь между теориями великого объединения и протяженными супергравитациями

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Il Nuovo Cimento A (1965-1970)

Summary

By using the intrinsic properties of the Lie groups of the extended supergravities (ESGs), a connection between ESGs in four space-time dimensions and a chain of grand unified theories (GUTs) is obtained. The chain of GUTs we get starts withSU 3×SU2×U1 and ends up withE 6 (immersed in theE 7 group of the maximally extended supergravity). As by-products of our analysis we obtain a new approach to the (spin 1/2) fermions of a GUT as well as a possible solution for the generation problem. Finally, we discuss the implications of our analysis on the space-time content of an arbitrary GUT.

Riassunto

Usando le proprietà intrinseche dei gruppi di Lie delle supergravità estese (ESGs) si ottiene una connessione tra ESGs in quattro dimensioni spazio-tempo e una catena di teorie della grande unificazione (GUTs). La catena ottenuta di GUTs parte daSU 3×SU2×U1 e termina conE 6 (assorbito nel gruppoE 7 della supergravità estesa in modo massimale). Come sottoprodotti dall’analisi si ottengono un nuovo approccio ai fermioni (con spin 1/2) di una GUT ed anche una soluzione possibile del problema della generazione. Infine si discutono le applicazioni della nostra analisi al contenuto in spazio-tempo di un arbitrario GUT.

Резюме

Используя характерные свойства групп Ли для протяженных супергравитаций, получается связь между протяженными супергравитациями в четырех пространственно-временных измерениях и цепочкой теорий великого объединения. Для получения цепочки теорий великого объединения мы начинаем сSU 3×SU2×U1 ги заканчиваетE 6 (погруженной в группуE 7 для максимально протяженной супергравитации). Как побочный результат нашего анализа, мы получаем новый подход к фермионам (со спином половина) теории великого объединения, а также возможное решение проблемы образования. В заключение мы обсуждаем следствия нашего анализа для пространственно-временного содержания произвольной теории великого объединения.

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References

  1. Proceedings of the Europhysics Study Conference on Unification of Fundamental Interactions, Erice, 1980, edited byS. Ferrara, J. Ellis andP. Van Nieuwenhuizen (New York, N. Y., 1980).

  2. See,e.g.,H. Georgi: lectures at theFourth Kyoto Summer Institute on Grand Unified Theories and Related Topics, June 29–July 3, 1981 (to be published), and references therein.

  3. J. Ellis, M. K. Gaillard, L. Maiani andB. Zumino: inProceedings of the Europhysics Study Conference on Unification of Fundamental Interactions, Erice, 1980, edited byS. Ferrara, J. Ellis andP. Van Nieuwenhuizen (New York, N. Y., 1980), p. 69.

  4. J. Ellis, M. K. Gaillard andB. Zumino:Phys. Lett. B,94, 343 (1980).

    Article  ADS  Google Scholar 

  5. S. Helgason:Differential Geometry, Lie Groups, and Symmetric Spaces (New York, N. Y., 1978).

  6. See,e.g.,S. S. Chen:Complex Manifolds without Potential Theory (Princeton, N. J., 1967).

  7. See,e.g.,B.-Y. Chen andT. Nagano:Duke Math. J.,45, 405 (1978), and references therein.

    Article  MathSciNet  MATH  Google Scholar 

  8. See,e.g.,R. Hermann:Quantum and Fermion Differential Geometry (Brookline, Mass., 1978).

  9. E. Calabi andE. Vesentini:Ann. Math. (N. Y.),71, 472 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Nakagawa andR. Takagi:J. Math. Soc. Jpn.,28, 638 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  11. See,e.g.,D. Husemoller:Fiber Bundles (New York, N. Y., Heidelberg and Berlin, 1975).

  12. E. Cartan:Oeuvres Completes, Part 1, Vol.2 (Paris, 1952).

  13. J. A. Wolf andA. Korányi:Am. J. Math.,87, 899 (1965).

    Article  MATH  Google Scholar 

  14. See,e.g.,T. Ochiai:Trans. Am. Math. Soc.,152, 159 (1970), and references therein.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Max Planck Institute, D-183, Starnberg, Germany

    P. Tataru-Mihai

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  1. P. Tataru-Mihai
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Traduzione a cura della Redazione.

Перевебено ребакцией.

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Tataru-Mihai, P. A connection between grand unified theories and extended supergravities. Nuov Cim A 68, 56–64 (1982). https://doi.org/10.1007/BF02902734

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  • DOI: https://doi.org/10.1007/BF02902734

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