Radiatively induced spontaneous symmetry breaking for asymptotically free gauge theories

Eldad Gildener

doi:10.1103/PhysRevD.13.1025

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Radiatively induced spontaneous symmetry breaking for asymptotically free gauge theories

Eldad Gildener

Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

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Phys. Rev. D 13, 1025 – Published 15 February, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.1025

Abstract

We investigate the possibility that the symmetry of asymptotically free theories whose effective scalar quartic coupling constants (in the sense of the renormalization group) take on negative values is dynamically spontaneously broken. We find this phenomenon to be common for theories whose scalars transform as the irreducible second-rank tensor representations of $SU (n)$ and $O (n)$ . The symmetry-breaking pattern is determined by the tree approximation in some cases, by the one-loop approximation in other cases, but for none of these models does it allow for an asymptotically free theory whose $S$ -matrix elements are defined. Our dynamical mechanism does provide a natural explanation of superstrong spontaneous symmetry breaking.

References (18)

E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973)
D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)
H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973)
S. Coleman, in Laws of Hadronic Matter, proceedings of the 1973 International Summer School "Ettore Majorana," Erice, Italy, edited by A. Zichichi (Academic, New York, 1975)
D. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973)
T. P. Cheng, E. Eichten, and L. F. Li, Phys. Rev. D 9, 2259 (1974)
[5,6] E. Ma, Phys. Rev. D 11, 322 (1975) N. P. Chang, ibid. 10, 2076 (1974) M. Suzuki, Nucl. Phys. B83, 269 (1974)
[9]
S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973)
S. Coleman, in Properties of the Fundamental Interactions, proceedings of the 1971 International Summer School "Ettore Majorana," Erice, Italy, 1971, edited by A. Zichichi (Editrice Compositori, Bologna, 1973)
F. J. Dyson, Phys. Rev. 75, 486 (1949) ibid.75, 1736 (1949)
S. Coleman and D. J. Gross, Phys. Rev. Lett. 31, 851 (1973)
[4]
H. Georgi and S. Glashow, Phys. Rev. D 6, 2977 (1972)
S. Weinberg, Phys. Rev. Lett. 29, 1698 (1972)
L. F. Li, Phys. Rev. D 9, 1723 (1974)
R. Jackiw and K. Johnson, Phys. Rev. D 8, 2386 (1973) J. Cornwall and R. Norton, ibid. 8, 3338 (1973)
S. Weinberg, Phys. Rev. Lett. 31, 494 (1973)

[c1] E. S. Abers and B. W. Lee, Phys. Rep. 9C, 1 (1973)

[c2] D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)

[c3] H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973)

[c4] S. Coleman, in Laws of Hadronic Matter, proceedings of the 1973 International Summer School "Ettore Majorana," Erice, Italy, edited by A. Zichichi (Academic, New York, 1975)

[c5] D. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973)

[c6] T. P. Cheng, E. Eichten, and L. F. Li, Phys. Rev. D 9, 2259 (1974)

[c7] [5,6] E. Ma, Phys. Rev. D 11, 322 (1975) N. P. Chang, ibid. 10, 2076 (1974) M. Suzuki, Nucl. Phys. B83, 269 (1974)

[c8] [9]

[c9] S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973)

[c10] S. Coleman, in Properties of the Fundamental Interactions, proceedings of the 1971 International Summer School "Ettore Majorana," Erice, Italy, 1971, edited by A. Zichichi (Editrice Compositori, Bologna, 1973)

[c11] F. J. Dyson, Phys. Rev. 75, 486 (1949) ibid.75, 1736 (1949)

[c12] S. Coleman and D. J. Gross, Phys. Rev. Lett. 31, 851 (1973)

[c13] [4]

[c14] H. Georgi and S. Glashow, Phys. Rev. D 6, 2977 (1972)

[c15] S. Weinberg, Phys. Rev. Lett. 29, 1698 (1972)

[c16] L. F. Li, Phys. Rev. D 9, 1723 (1974)

[c17] R. Jackiw and K. Johnson, Phys. Rev. D 8, 2386 (1973) J. Cornwall and R. Norton, ibid. 8, 3338 (1973)

[c18] S. Weinberg, Phys. Rev. Lett. 31, 494 (1973)

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Radiatively induced spontaneous symmetry breaking for asymptotically free gauge theories

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