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UFN, 1985, Volume 146, Number 4, Pages 655–681 (Mi ufn8347)  

This article is cited in 17 scientific papers (total in 17 papers)


Supersymmetry: Kaluza–Klein theory, anomalies, and superstrings

I. Ya. Aref'eva, I. V. Volovich

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Progress in the search for a unified theory of elementary particles is reviewed. The supersymmetrical Kaluza-Klein theories are described: 11-, 10-, and 6-dimensional models of supergravity. The methods of spontaneous compactification, with whose help the four-dimensional theories are obtained, are described. The properties of the massless sectorzero modes in the Kaluza–Klein theories–and the question of the stability of vacuum solutions are discussed. An important criterion for the selection of a self-consistent theory is the absence of anomalies. The basic formulas for multidimensional chiral and gravitational anomalies are presented. The mechanism of the cancellation of the anomaly for Green and Schwarz's 10-dimensional effective field theory of superstrings with the gauge groups SO(32) and E$_8\times$ E$_8$ is described. The basic concepts and the results of the theory of superstrings are presented. This theory has no divergences and is at the present time a very attractive candidate for a unified theory of elementary particles.


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English version:
Physics–Uspekhi, 1985, 28:8, 694–708

UDC: 539.12.01
PACS: 04.50.+h, 11.30.Pb, 11.25.Mj, 04.65.+e, 11.30.Ly, 11.30.Rd

Citation: I. Ya. Aref'eva, I. V. Volovich, “Supersymmetry: Kaluza–Klein theory, anomalies, and superstrings”, UFN, 146:4 (1985), 655–681; Phys. Usp., 28:8 (1985), 694–708

Citation in format AMSBIB
\by I.~Ya.~Aref'eva, I.~V.~Volovich
\paper Supersymmetry: Kaluza--Klein theory, anomalies, and superstrings
\jour UFN
\yr 1985
\vol 146
\issue 4
\pages 655--681
\jour Phys. Usp.
\yr 1985
\vol 28
\issue 8
\pages 694--708

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    This publication is cited in the following articles:
    1. I. Ya. Aref'eva, I. V. Volovich, “Covariant quantization of gauge-invariant string field theories”, Theoret. and Math. Phys., 67:2 (1986), 521–524  mathnet  crossref  mathscinet  isi
    2. I. Ya. Aref'eva, I. V. Volovich, B. G. Dragovich, “Spontaneous reduction in multidimensional ($D=10, 11$) supergravity theories with arbitrary signature”, Theoret. and Math. Phys., 70:3 (1987), 297–304  mathnet  crossref  mathscinet  isi
    3. A. D. Popov, “Hidden symmetries of Kaluza–Klein theories”, Theoret. and Math. Phys., 71:1 (1987), 385–392  mathnet  crossref  mathscinet  isi
    4. A. D. Popov, “Spontaneous compactification of $d=11$ supergravity due to Rarita–Schwinger fields”, Theoret. and Math. Phys., 71:2 (1987), 553–555  mathnet  crossref  mathscinet  isi
    5. I. V. Volovich, “$p$-adic space-time and string theory”, Theoret. and Math. Phys., 71:3 (1987), 574–576  mathnet  crossref  mathscinet  zmath  isi
    6. V. S. Vladimirov, “Generalized functions over the field of $p$-adic numbers”, Russian Math. Surveys, 43:5 (1988), 19–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. D. Popov, “Chiral fermions in $d=11$ supergravity with additional time dimensions”, Theoret. and Math. Phys., 76:1 (1988), 718–724  mathnet  crossref  mathscinet  isi
    8. A. D. Popov, “Chiral fermions in $N=2$, $d=10$ supergravity with additional time dimensions”, Theoret. and Math. Phys., 74:2 (1988), 145–149  mathnet  crossref  mathscinet  isi
    9. M. O. Katanaev, “String with dynamical geometry. Hamiltonian analysis in conformal gauge”, Theoret. and Math. Phys., 80:2 (1989), 838–848  mathnet  crossref  mathscinet  isi
    10. S. D. Odyntsov, “Vilkovisky effective action in quantum gravity with matter”, Theoret. and Math. Phys., 82:1 (1990), 45–51  mathnet  crossref  mathscinet  isi
    11. D. V. Vassilevich, V. D. Lyakhovsky, N. N. Shtykov, “De Witt–Schwinger coefficients for projective and Grassmann manifolds”, Theoret. and Math. Phys., 83:1 (1990), 339–346  mathnet  crossref  mathscinet  isi
    12. A. D. Popov, “Geometric quantization of strings and reparametrization invariance”, Theoret. and Math. Phys., 83:3 (1990), 608–619  mathnet  crossref  mathscinet  isi
    13. T. A. Ivanova, A. D. Popov, “(Anti)self-dual gauge fields in dimension $d\ge 4$”, Theoret. and Math. Phys., 94:2 (1993), 225–242  mathnet  crossref  mathscinet  zmath  isi
    14. Z. Kh. Zakirova, “Rigid six-dimensional $h$-spaces of constant curvature”, Theoret. and Math. Phys., 158:3 (2009), 293–299  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. D. S. Shirokov, “Pauli theorem in the description of $n$-dimensional spinors in the Clifford algebra formalism”, Theoret. and Math. Phys., 175:1 (2013), 454–474  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. M. G. Ivanov, “Formulation of quantum mechanics with dynamical time”, Proc. Steklov Inst. Math., 285 (2014), 145–156  mathnet  crossref  crossref  isi  elib  elib
    17. P. E. Brandyshev, “Spontaneous compactification of eleven-dimensional supergravity with higher-order corrections in the curvature”, Theoret. and Math. Phys., 188:1 (2016), 1099–1108  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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