Access by Xinjiang University

Non-Abelian vortices in Chern-Simons theories and their induced effective theory

L. G. Aldrovandi^1,2 and F. A. Schaposnik^2,3,*

¹CERN, Theory Division, CH-1211, Geneva 23, Switzerland.
²Departamento de Física, Universidad Nacional de La Plata, C.C. 67, (1900) La Plata, Argentina.
³CEFIMAS, Santa Fe 1145, C1059ABF - Buenos Aires, Argentina

^*F. A. S. is associated with CICBA.

Phys. Rev. D 76, 045010 – Published 21 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.045010

Abstract

Non-Abelian vortices for a supersymmetric $N = 2$ Chern-Simons-Higgs theory are explicitly constructed. We introduce $N$ Higgs fields in the fundamental representation of the $U (N)$ gauge group in order to have a color-flavor $S U (N)$ group remaining unbroken in the asymmetric phase. Bogomol’nyi-like first-order equations are found and rotationally symmetric solutions are proposed. These solutions are shown to be truly non-Abelian by parametrizing them in terms of orientational collective coordinates. The low-energy effective action for the orientational moduli results to be the one-dimensional supersymmetric $N = 2$ ${C P}^{N - 1}$ model. We analyze the quantum mechanics of this effective theory in the $N = 2$ case.

Article Text

References (36)

S. Deser, R. Jackiw, and S. Templeton, Phys. Rev. Lett. 48, 975 (1982).
S. Deser, R. Jackiw, and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982); 185, 406(E) (1988); 281, 409 (2000); 281, 409(E) (2000).
J. Frohlich and P. A. Marchetti, Commun. Math. Phys. 121, 177 (1989).
F. Wilczek, Fractional Statistics and Anyon Superconductivity (World Scientific, Singapore, 1990).
A. Lerda, Anyons: Quantum Mechanics of Particles with Fractional Statistics, Lecture Notes in Physics Vol. m14 (Springer, Berlin 1992).
S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989).
J. K. Jain, Phys. Rev. Lett. 63, 199 (1989).
S. C. Zhang, Int. J. Mod. Phys. B 6, 25 (1992).
G. Murthy and R. Shankar, arXiv:cond-mat/9802244.
G. V. Dunne, arXiv:hep-th/9902115.
E. B. Bogomolny, Yad. Fiz. 24, 861 (1976) [Sov. J. Nucl. Phys. 24, 449 (1976)].
J. Hong, Y. Kim, and P. Y. Pac, Phys. Rev. Lett. 64, 2230 (1990); R. Jackiw and E. J. Weinberg, ibid. 64, 2234 (1990).
R. Jackiw, K. M. Lee, and E. J. Weinberg, Phys. Rev. D 42, 3488 (1990).
K. M. Lee, Phys. Rev. Lett. 66, 553 (1991).
H. J. de Vega F. A. Schaposnikand , Phys. Rev. Lett. 56, 2564 (1986).
H. J. de Vega and F. A. Schaposnik, Phys. Rev. D 34, 3206 (1986).
L. F. Cugliandolo, G. Lozano, M. V. Manias, and F. A. Schaposnik, Mod. Phys. Lett. A 6, 479 (1991).
A. Hanany and D. Tong, J. High Energy Phys. 07 (2003) 037.
R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi, and A. Yung, Nucl. Phys. B673, 187 (2003).
M. Shifman and A. Yung, Phys. Rev. D 70, 045004 (2004).
A. Hanany and D. Tong, J. High Energy Phys. 04 (2004) 066.
Y. Isozumi, M. Nitta, K. Ohashi, and N. Sakai, Phys. Rev. D 71, 065018 (2005).
A. Gorsky, M. Shifman, and A. Yung, Phys. Rev. D 71, 045010 (2005).
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi, and N. Sakai, Phys. Rev. Lett. 96, 161601 (2006).
M. Eto, Y. Isozumi, M. Nitta, K. Ohashi, and N. Sakai, J. Phys. A 39, R315 (2006).
B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975).
E. A. Ivanov, Phys. Lett. B 268, 203 (1991).
H. Nishino and S. J. J. Gates, Int. J. Mod. Phys. A 8, 3371 (1993).
S. J. J. Gates and H. Nishino, Phys. Lett. B 281, 72 (1992).
D. Olive and E. Witten, Phys. Lett. 78B, 97 (1978).
P. A. M. Dirac, Can. J. Math. 2, 129 (1950).
G. V. Dunne, Ann. Phys. (N.Y.) 215, 233 (1992).
R. Auzzi, M. Shifman, and A. Yung, Phys. Rev. D 73, 105012 (2006).
M. Eto, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci, and N. Yokoi, Phys. Rev. D 74, 065021 (2006).
E. Verlinde, in Modern Quantum Field Theory (World Scientific, Singapore, 1991).
E. Fradkin, C. Nayak, and K. Schoutens, Nucl. Phys. B546, 711 (1999).

Physical Review D

Export citation

Export citation

Non-Abelian vortices in Chern-Simons theories and their induced effective theory

Abstract

Article Text

References (36)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation