Symmetry breaking in three-generation Calabi-Yau manifolds

Pran Nath; R. Arnowitt

doi:10.1103/PhysRevD.39.2006

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Symmetry breaking in three-generation Calabi-Yau manifolds

Pran Nath

R. Arnowitt

Department of Physics, Northeastern University, Boston, Massachusetts 02115

Center for Theoretical Physics, Department of Physics, Texas A&M University, College Station, Texas 77843

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Phys. Rev. D 39, 2006 – Published 1 April, 1989

DOI: https://doi.org/10.1103/PhysRevD.39.2006

Abstract

The spontaneous breaking of [SU(3) $]^{3}$ symmetry to SU(3)×SU(2)×U(1) due to nonrenormalizable interactions in the three-generation Calabi-Yau superstring model is considered. It is seen that these models lead naturally to intermediate scales $M_{I}$ ∼ $10^{15}$ GeV with simultaneous formation of N and $ν^{c}$ vacuum expectation values (VEV’s). The lowest-lying extrema automatically preserve matter parity and hence protect the model against too rapid proton decay. Models with matter parity also protect against electroweak Higgs VEV’s from forming at $M_{I}$ . The intermediate mass scale produces some particles with mass O( $M_{I}$ ). It also implies the existence of others with mass ∼1 TeV, which are possibly accessible to low-energy experiments.

References (15)

D. Gross, J. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 55, 502 (1985); Nucl. Phys. B258, 253 (1985).
See, e.g., D. Gross, talk at XXIV International Conference on High Energy Physics, Munich, 1988 (unpublished).
P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985).
B. Greene, K. H. Kirklin, P. J. Miron and G. G. Ross, Phys. Lett. B 180, 69 (1986); Nucl. Phys. B274, 574 (1986) ibid. B278, 667 (1986); ibid. B292, 606 (1987).
S. T. Yau, in Anomalies, Geometry, and Topology, proceedings of the Symposium, Argonne, Illinois, 1985, edited by W. A. Bardeen and A. R. White (World Scientific, Singapore, 1985), p. 395.
Y. Hosotani, Phys. Lett. 126B, 309 (1983); E. Witten, Nucl. Phys. B258, 75 (1985).
B. A. Campbell, K. A. Olive and D. Reiss, Nucl. Phys. B296, 129 (1986); J. Ellis, K. Enqvist, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B 188, 415 (1987); B. A. Campbell et al., Report No. CERN-TH. 4473/87 (unpublished); M. Dine and C. Lee, Phys. Lett. B 203, 371 (1988).
P. Candelas, Nucl. Phys. B298, 458 (1988); P. Candelas and S. Kalara, ibid. B298, 493 (1988); S. Kalara and R. N. Mohapatra, Phys. Rev. D 36, 3474 (1987); B. R. Greene, K. H. Kirklin, P. J. Miron and G. G. Ross, Phys. Lett. B 192, 111 (1987); J. Distler, B. G. Greene, K. H. Kirklin and P. J. Miron, ibid. 195, 41 (1987).
J. Distler and B. Greene, Nucl. Phys. B309, 295 (1988); D. Gepner, Princeton Report No. PUPT-1093, 1988 (unpublished); C. A. Lütken and G. G. Ross, Report No. CERN-TH. 5132/88, 1988 (unpublished).
M. C. Bento, L. Hall and G. G. Ross, Nucl. Phys. B292, 400 (1987).
R. Arnowitt and P. Nath, Phys. Rev. Lett. 60, 1817 (1988).
R. Arnowitt and P. Nath, Report No. CTP-TAMU-74/88-NUB-2960 (unpublished).
That this may be expected to occur at $M_{I}$ app $10^{15}$ GeV has been shown recently for simple models by F. del Agiula and G. D. Coughlan, Report No. CERN-TH. 5143/88-UAB-FT-195/88 (unpublished).
A degenerate extrema with $N_{1}$ <-> $N_{2}$ , $ν_{1}^{c}$ <-> $ν_{2}^{c}$ of course also exists since Eqs. (3.4) treat the C-even and C-odd multiplets symmetrically in our simplified model. This degeneracy would presumably be removed when couplings between multiplets are included.
S. Weinberg, Phys. Rev. D 26, 287 (1982).

[c1] D. Gross, J. Harvey, E. Martinec and R. Rohm, Phys. Rev. Lett. 55, 502 (1985); Nucl. Phys. B258, 253 (1985).

[c2] See, e.g., D. Gross, talk at XXIV International Conference on High Energy Physics, Munich, 1988 (unpublished).

[c3] P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258, 46 (1985).

[c4] B. Greene, K. H. Kirklin, P. J. Miron and G. G. Ross, Phys. Lett. B 180, 69 (1986); Nucl. Phys. B274, 574 (1986) ibid. B278, 667 (1986); ibid. B292, 606 (1987).

[c5] S. T. Yau, in Anomalies, Geometry, and Topology, proceedings of the Symposium, Argonne, Illinois, 1985, edited by W. A. Bardeen and A. R. White (World Scientific, Singapore, 1985), p. 395.

[c6] Y. Hosotani, Phys. Lett. 126B, 309 (1983); E. Witten, Nucl. Phys. B258, 75 (1985).

[c7] B. A. Campbell, K. A. Olive and D. Reiss, Nucl. Phys. B296, 129 (1986); J. Ellis, K. Enqvist, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B 188, 415 (1987); B. A. Campbell et al., Report No. CERN-TH. 4473/87 (unpublished); M. Dine and C. Lee, Phys. Lett. B 203, 371 (1988).

[c8] P. Candelas, Nucl. Phys. B298, 458 (1988); P. Candelas and S. Kalara, ibid. B298, 493 (1988); S. Kalara and R. N. Mohapatra, Phys. Rev. D 36, 3474 (1987); B. R. Greene, K. H. Kirklin, P. J. Miron and G. G. Ross, Phys. Lett. B 192, 111 (1987); J. Distler, B. G. Greene, K. H. Kirklin and P. J. Miron, ibid. 195, 41 (1987).

[c9] J. Distler and B. Greene, Nucl. Phys. B309, 295 (1988); D. Gepner, Princeton Report No. PUPT-1093, 1988 (unpublished); C. A. Lütken and G. G. Ross, Report No. CERN-TH. 5132/88, 1988 (unpublished).

[c10] M. C. Bento, L. Hall and G. G. Ross, Nucl. Phys. B292, 400 (1987).

[c11] R. Arnowitt and P. Nath, Phys. Rev. Lett. 60, 1817 (1988).

[c12] R. Arnowitt and P. Nath, Report No. CTP-TAMU-74/88-NUB-2960 (unpublished).

[c13] That this may be expected to occur at $M_{I}$ app $10^{15}$ GeV has been shown recently for simple models by F. del Agiula and G. D. Coughlan, Report No. CERN-TH. 5143/88-UAB-FT-195/88 (unpublished).

[c14] A degenerate extrema with $N_{1}$ <-> $N_{2}$ , $ν_{1}^{c}$ <-> $ν_{2}^{c}$ of course also exists since Eqs. (3.4) treat the C-even and C-odd multiplets symmetrically in our simplified model. This degeneracy would presumably be removed when couplings between multiplets are included.

[c15] S. Weinberg, Phys. Rev. D 26, 287 (1982).

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Symmetry breaking in three-generation Calabi-Yau manifolds

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