Gauge symmetry enhancement and radiatively induced mass in the large <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math></span> nonlinear sigma model

Taichi Itoh; Phillial Oh; Cheol Ryou

doi:10.1103/PhysRevD.64.045005

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Gauge symmetry enhancement and radiatively induced mass in the large $N$ nonlinear sigma model

Taichi Itoh^*

Phillial Oh^† and Cheol Ryou^‡

Department of Physics, Kyungpook National University, Taegu 702-701, Korea

Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, Korea

^*E-mail address: taichi@knu.ac.kr
^†E-mail address: ploh@dirac.skku.ac.kr
^‡E-mail address: cheol@newton.skku.ac.kr

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Phys. Rev. D 64, 045005 – Published 19 July, 2001

DOI: https://doi.org/10.1103/PhysRevD.64.045005

Abstract

We consider a hybrid of nonlinear sigma models in which two complex projective spaces are coupled with each other under a duality. We study the large N effective action in 1+1 dimensions. We find that some of the dynamically generated gauge bosons acquire radiatively induced masses which, however, vanish along the self-dual points where the two couplings characterizing each complex projective space coincide. These points correspond to the target space of the Grassmann manifold along which the gauge symmetry is enhanced, and the theory favors the non-Abelian ultraviolet fixed point.

References (17)

M. Bando, T. Kugo, and K. Yamawaki, Phys. Rep. 164, 217 (1988).
W. J. Zakrzewski, Low Dimensional Sigma Models (IOP, Bristol, 1989).
S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985); A. M. Polyakov, Gauge Fields and Strings (Harwood, Chur, Switzerland, 1987).
W. A. Bardeen, B. W. Lee, and R. E. Shrock, Phys. Rev. D 14, 985 (1976).
I. Ya. Aref’eva and S. I. Azakov, Nucl. Phys. B162, 298 (1980); I. Ya. Aref’eva, Ann. Phys. (N.Y.) 117, 393 (1979).
T. Itoh and P. Oh, Phys. Lett. B 491, 362 (2000); Phys. Rev. D 63, 025019 (2001).
H. Eichenherr, Nucl. Phys. B146, 215 (1978); V. Golo and A. Perelomov, Phys. Lett. 79B, 112 (1978); A. D’Adda, P. Di Vecchia, and M. Lüscher, Nucl. Phys. B146, 63 (1978); ibid.E. Witten, B149, 285 (1979).
R. D. Pisarski, Phys. Rev. D 20, 3358 (1979); E. Brezin, S. Hikami, and J. Zinn-Justin, Nucl. Phys. B165, 528 (1980).
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic, New York, 1978).
E. Cava, R. Jengo, and C. Omero, Nucl. Phys. B158, 381 (1979); ibid.S. Duane, B168, 32 (1980); G. Duerksen, Phys. Rev. D 24, 926 (1981); M. Bando, Y. Taniguchi and S. Tanimura, Prog. Theor. Phys. 97, 665 (1997).
This Lagrangian was considered for $r = 1$ in A. J. Macfarlane, Phys. Lett. 82B, 239 (1979). For our purposes, it is essential to keep r arbitrary from the beginning.
E. Cremmer and B. Julia, Phys. Lett. 80B, 48 (1978); Nucl. Phys. B159, 141 (1979); A. P. Balachandran, A. Stern, and C. G. Trahern, Phys. Rev. D 19, 2416 (1979); M. Bando, T. Kugo, and K. Yamawaki, Prog. Theor. Phys. 73, 1541 (1985).
T. Itoh, P. Oh, and C. Ryou, hep-th/0104204.
We stress that the nomenclature “symmetry reduction” here stands for the gauge symmetry away from the self-dual points being smaller than that along these points with $r = 1$ . We simply compare the gauge symmetries for different values of r each of which corresponds to a different theory. This is not the usual dynamical Higgs mechanism in which we compare different phases for a fixed r.
See R. Jackiw, Int. J. Mod. Phys. B 14, 2011 (2000), and references therein.
M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1987), Vols. I and II; J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998), Vols. I and II.
A. Giveon, M. Porrati, and E. Rabinovici, Phys. Rep. 244, 77 (1994).

[c1] M. Bando, T. Kugo, and K. Yamawaki, Phys. Rep. 164, 217 (1988).

[c2] W. J. Zakrzewski, Low Dimensional Sigma Models (IOP, Bristol, 1989).

[c3] S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985); A. M. Polyakov, Gauge Fields and Strings (Harwood, Chur, Switzerland, 1987).

[c4] W. A. Bardeen, B. W. Lee, and R. E. Shrock, Phys. Rev. D 14, 985 (1976).

[c5] I. Ya. Aref’eva and S. I. Azakov, Nucl. Phys. B162, 298 (1980); I. Ya. Aref’eva, Ann. Phys. (N.Y.) 117, 393 (1979).

[c6] T. Itoh and P. Oh, Phys. Lett. B 491, 362 (2000); Phys. Rev. D 63, 025019 (2001).

[c7] H. Eichenherr, Nucl. Phys. B146, 215 (1978); V. Golo and A. Perelomov, Phys. Lett. 79B, 112 (1978); A. D’Adda, P. Di Vecchia, and M. Lüscher, Nucl. Phys. B146, 63 (1978); ibid.E. Witten, B149, 285 (1979).

[c8] R. D. Pisarski, Phys. Rev. D 20, 3358 (1979); E. Brezin, S. Hikami, and J. Zinn-Justin, Nucl. Phys. B165, 528 (1980).

[c9] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic, New York, 1978).

[c10] E. Cava, R. Jengo, and C. Omero, Nucl. Phys. B158, 381 (1979); ibid.S. Duane, B168, 32 (1980); G. Duerksen, Phys. Rev. D 24, 926 (1981); M. Bando, Y. Taniguchi and S. Tanimura, Prog. Theor. Phys. 97, 665 (1997).

[c11] This Lagrangian was considered for $r = 1$ in A. J. Macfarlane, Phys. Lett. 82B, 239 (1979). For our purposes, it is essential to keep r arbitrary from the beginning.

[c12] E. Cremmer and B. Julia, Phys. Lett. 80B, 48 (1978); Nucl. Phys. B159, 141 (1979); A. P. Balachandran, A. Stern, and C. G. Trahern, Phys. Rev. D 19, 2416 (1979); M. Bando, T. Kugo, and K. Yamawaki, Prog. Theor. Phys. 73, 1541 (1985).

[c13] T. Itoh, P. Oh, and C. Ryou, hep-th/0104204.

[c14] We stress that the nomenclature “symmetry reduction” here stands for the gauge symmetry away from the self-dual points being smaller than that along these points with $r = 1$ . We simply compare the gauge symmetries for different values of r each of which corresponds to a different theory. This is not the usual dynamical Higgs mechanism in which we compare different phases for a fixed r.

[c15] See R. Jackiw, Int. J. Mod. Phys. B 14, 2011 (2000), and references therein.

[c16] M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1987), Vols. I and II; J. Polchinski, String Theory (Cambridge University Press, Cambridge, 1998), Vols. I and II.

[c17] A. Giveon, M. Porrati, and E. Rabinovici, Phys. Rep. 244, 77 (1994).

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Gauge symmetry enhancement and radiatively induced mass in the large $N$ nonlinear sigma model

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Gauge symmetry enhancement and radiatively induced mass in the large N nonlinear sigma model

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References (17)

Gauge symmetry enhancement and radiatively induced mass in the large $N$ nonlinear sigma model