- Access by Xinjiang University
Emergence of the Skyrme crystal in Gross-Neveu and ’t Hooft models at finite density
Phys. Rev. D 62, 096002 – Published 25 September, 2000
DOI: https://doi.org/10.1103/PhysRevD.62.096002
Abstract
We study two-dimensional, large N field theoretic models (Gross-Neveu model, ’t Hooft model) at finite baryon density near the chiral limit. The same mechanism which leads to massless baryons in these models induces a breakdown of translational invariance at any finite density. In the chiral limit baryonic matter is characterized by a spatially varying chiral angle with a wave number depending only on the density. For small bare quark masses a sine-Gordon kink chain is obtained which may be regarded as the simplest realization of the Skyrme crystal for nuclear matter. Characteristic differences between confining and non-confining models are pointed out.
References (47)
- M. Alford, K. Rajagopal, and F. Wilczek, Phys. Lett. B 422, 247 (1998).
- R. Rapp, T. Schäfer, E.V. Shuryak, and M. Velkovsky, Phys. Rev. Lett. 81, 53 (1998).
- Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
- D.J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).
- G. ’t Hooft, Nucl. Phys. B75, 461 (1974).
- G. ’t Hooft, Nucl. Phys. B72, 461 (1974).
- B.J. Harrington and A. Yildiz, Phys. Rev. D 11, 779 (1975).
- R.F. Dashen, S. Ma, and R. Rajaraman, Phys. Rev. D 11, 1499 (1975).
- U. Wolff, Phys. Lett. 157B, 303 (1985).
- T.F. Treml, Phys. Rev. D 39, 679 (1989).
- A. Barducci, R. Casalbuoni, M. Modugno, G. Pettini, and R. Gatto, Phys. Rev. D 51, 3042 (1995).
- L.D. McLerran and A. Sen, Phys. Rev. D 32, 2794 (1985).
- Ming Li, Phys. Rev. D 34, 3888 (1986).
- V. Schön and M. Thies, Phys. Lett. B 481, 299 (2000).
- I. Affleck, Nucl. Phys. B265, 448 (1986).
- L.L. Salcedo, S. Levit, and J.W. Negele, Nucl. Phys. B361, 585 (1991).
- F. Lenz, M. Thies, S. Levit, and K. Yazaki, Ann. Phys. (N.Y.) 208, 1 (1991).
- W. Fischler, J. Kogut, and L. Susskind, Phys. Rev. D 19, 1188 (1979).
- Y-Ch. Kao and Y-W. Lee, Phys. Rev. D 50, 1165 (1994).
- H.R. Christiansen and F.A. Schaposnik, Phys. Rev. D 55, 4920 (1997).
- D.V. Deryagin, D.Yu. Grigoriev, and V.A. Rubakov, Int. J. Mod. Phys. A 7, 659 (1992).
- E. Shuster and D.T. Son, Nucl. Phys. B573, 434 (2000).
- B-Y. Park, M. Rho, A. Wirzba, and I. Zahed, Phys. Rev. D 62, 034015 (2000).
- M. Kutschera, W. Broniowski, and A. Kotlorz, Nucl. Phys. A516, 566 (1990).
- M. Sadzikowski and W. Broniowski, hep-ph/0003282.
- S. Coleman, Commun. Math. Phys. 31, 259 (1973).
- N.D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
- E. Witten, Nucl. Phys. B145, 110 (1978).
- V.L. Berezinsky, Zh. Éksp. Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1971)].
- J.M. Kosterlitz and D. Thouless, J. Phys. C 6, 1181 (1973).
- T.H.R. Skyrme, Proc. R. Soc. London A260, 127 (1961).
- I. Klebanov, Nucl. Phys. B262, 133 (1985).
- R. Pausch, M. Thies, and V.L. Dolman, Z. Phys. A 338, 441 (1991).
- E. Witten, Nucl. Phys. B160, 57 (1979).
- J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. Lett. 34, 1353 (1975).
- A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, and V.F. Weisskopf, Phys. Rev. D 9, 3471 (1974).
- I. Bars and M.B. Green, Phys. Rev. D 17, 537 (1978).
- Ming Li, L. Wilets, and M.C. Birse, J. Phys. G 13, 915 (1987).
- A.R. Zhitnitsky, Phys. Lett. 165B, 405 (1985).
- E. Abdalla and M.C.B. Abdalla, Phys. Rep. 265, 253 (1996).
- T.T. Wu, Phys. Lett. 71B, 142 (1977).
- A.C. Scott, F.Y.F. Chu, and D.W. McLaughlin, Proc. IEEE 61, 1443 (1973).
- M. Gell-Mann, R.J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968).
- W.L. McMillan, Phys. Rev. B 16, 4655 (1977).
- G. Theodorou and T.M. Rice, Phys. Rev. B 18, 2840 (1978).
- K. Takayama and M. Oka, Nucl. Phys. A551, 637 (1993).
- Handbook of Mathematical Functions, edited by M. Abramovitz and I.A. Stegun (Dover, New York, 1970).