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Abstract:

In this paper we establish the existence of vortex solutions for a Chern-Simons-Higgs model with gauge group SU(. N). ×. U(1) and flavor SU(. N). These symmetries ensure the existence of genuine non-Abelian vortices through a color-flavor locking. Under a suitable ansatz we reduce the problem to a 2. ×. 2 system of nonlinear elliptic equations with exponential terms. We study this system over the full plane and over a doubly periodic domain, respectively. For the planar case we use a variational argument to establish the existence result and derive the decay estimates of the solutions. Over the doubly periodic domain we show that the system admits at least two gauge-distinct solutions carrying the same physical energy by using a constrained minimization approach and the mountain-pass theorem. In both cases we get the quantized vortex magnetic fluxes and electric charges. © 2015 Elsevier Inc..

Registro:

Documento: Artículo
Título:Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor
Autor:Chen, S.; Han, X.; Lozano, G.; Schaposnik, F.A.
Filiación:Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, Henan, 475004, China
Taida Institute for Mathematical Sciences, Center for Advanced Study in Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan
Departamento de Física e Instituto de Física de Buenos Aires, FCEyN, Pabellón 1, Ciudad Universitaria, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Departamento de Física, Universidad Nacional de La Plata, Instituto de Física La Plata, C.C. 67, La Plata, 1900, Argentina
Palabras clave:BPS equations; Chern-Simons-Higgs equations; Doubly periodic solutions; Existence theorems; Topological solutions
Año:2015
Volumen:259
Número:6
Página de inicio:2458
Página de fin:2498
DOI: http://dx.doi.org/10.1016/j.jde.2015.03.037
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v259_n6_p2458_Chen

Referencias:

  • Abrikosov, A.A., On the magnetic properties of superconductors of the second group (1957) Sov. Phys. JETP, 5, pp. 1174-1182
  • Adams, R.A., Fournier, J.F., Sobolev Spaces (2003) Pure and Applied Mathematics, 140. , Elsevier, Amsterdam
  • Aharony, O., Gur-Ari, G., Yacoby, R., Correlation functions of large N Chern-Simons matter theories and bosonization in three dimensions (2012) J. High Energy Phys., 1212, p. 028
  • Aharony, O., Bergman, O., Jafferis, D.L., Maldacena, J., N=6 superconformal Chern-Simons matter theories, M2-branes and their gravity duals (2008) J. High Energy Phys., 91, p. 0810
  • Ambrosetti, A., Rabinowitz, P., Dual variational methods in critical point theory and applications (1973) J. Funct. Anal., 14, pp. 349-381
  • Aubin, T., (1982) Nonlinear Analysis on Manifolds: Monge-Ampére Equations, , Springer, Berlin and New York
  • Auzzi, R., Kumar, S., Non-abelian vortices at weak and strong coupling in mass deformed ABJM theory (2009) J. High Energy Phys., 71, p. 10
  • Bogomol'nyi, E.B., The stability of classical solitons (1976) Sov. J. Nucl. Phys., 24, pp. 449-454
  • Bradlow, S.B., Vortices in holomorphic line bundles over closed Kahler manifolds (1990) Comm. Math. Phys., 135, pp. 1-17
  • Caffarelli, L.A., Yang, Y., Vortex condensation in the Chern-Simons-Higgs model: an existence theorem (1995) Comm. Math. Phys., 168, pp. 321-336
  • Chen, S., Zhang, R., Zhu, M., Multiple vortices in the Aharony-Bergman-Jafferis-Maldacena model (2013) Ann. Henri Poincaré, 14, pp. 1169-1192
  • Chen, R.M., Guo, Y., Spirn, D., Yang, Y., Electrically and magnetically charged vortices in the Chern-Simons-Higgs theory (2009) Proc. R. Soc. Lond. Ser. A, 465, pp. 3489-3516
  • Cugliandolo, L.F., Lozano, G., Manias, M.V., Schaposnik, F.A., Bogomolny equations for non-Abelian Chern-Simons-Higgs theories (1991) Modern Phys. Lett. A, 6, pp. 479-486
  • Deser, S., Jackiw, R., Templeton, S., Three-dimensional massive gauge theories (1982) Phys. Rev. Lett., 48, pp. 975-978
  • Deser, S., Jackiw, R., Templeton, S., Topologically massive gauge theories (1982) Ann. Physics, 140, pp. 372-411
  • de Vega, H.J., Schaposnik, F.A., A classical vortex solution of the Abelian Higgs model (1976) Phys. Rev. D, 14, pp. 1100-1106
  • de Vega, H.J., Schaposnik, F.A., Electrically charged vortices in non-Abelian gauge theories with Chern-Simons term (1986) Phys. Rev. Lett., 56, pp. 2564-2566
  • de Vega, H.J., Schaposnik, F.A., Vortices and electrically charged vortices in non-Abelian gauge theories (1986) Phys. Rev. D, 34, pp. 3206-3213
  • Fontana, L., Sharp borderline Sobolev inequalities on compact Riemannian manifolds (1993) Comment. Math. Helv., 68, pp. 415-454
  • Fradkin, E.H., Schaposnik, F.A., The Fermion-boson mapping in three-dimensional quantum field theory (1994) Phys. Lett. B, 338, pp. 253-258
  • Frohlich, J., Zee, A., Large scale physics of the quantum Hall fluid (1991) Nuclear Phys. B, 364, pp. 517-540
  • Ghoussoub, N., (1993) Duality and Perturbation Methods in Critical Point Theory, , Cambridge University Press, Cambridge
  • González-Arroyo, A., Nonperturbative quantum field physics (1998) Proceedings, Advanced School, , World Scientific, Singapore, M. Asorey, A. Dobado (Eds.)
  • Han, X., Lin, C.-S., Tarantello, G., Yang, Y., Chern-Simons vortices in the Gudnason model (2014) J. Funct. Anal., 267, pp. 678-726
  • Han, X., Tarantello, G., Doubly periodic self-dual vortices in a relativistic non-Abelian Chern-Simons model (2014) Calc. Var. Partial Differential Equations, 49, pp. 1149-1176
  • Han, X., Yang, Y., Existence theorems for vortices in the Aharony-Bergman-Jafferis-Maldacena model (2015) Comm. Math. Phys., 333, pp. 229-259
  • Harden, J.L., Arp, V., The lower critical field in the Ginzburg-Landau theory of superconductivity (1963) Cryogenics, 3, pp. 105-108
  • 't Hooft, G., A property of electric and magnetic flux in non-Abelian gauge theories (1979) Nuclear Phys. B, 153, pp. 141-160
  • Hong, J., Kim, Y., Pac, P.Y., On the multivortex solutions of the Abelian Chern-Simons-Higgs theory (1990) Phys. Rev. Lett., 64, pp. 2230-2233
  • Jackiw, R., Weinberg, E.J., Self-dual Chern-Simons vortices (1990) Phys. Rev. Lett., 64, pp. 2234-2237
  • Jaffe, A., Taubes, C.H., (1980) Vortices and Monopoles, , Birkhäuser, Boston
  • Kim, C., Kim, Y., Kwon, O.K., Nakajima, H., Vortex-type half-BPS solitons in ABJM theory (2009) Phys. Rev. D, 80, p. 045013
  • Lieb, E.H., Yang, Y., Non-Abelian vortices in supersymmetric gauge field theory via direct methods (2012) Comm. Math. Phys., 313, pp. 445-478
  • Lozano, G.S., Marques, D., Moreno, E.F., Schaposnik, F.A., Non-Abelian Chern-Simons vortices (2007) Phys. Lett. B, 654, p. 27
  • Lozano, G.S., Marques, D., Schaposnik, F.A., Non-Abelian vortices on the torus (2007) J. High Energy Phys., 709, p. 095
  • Manton, N., Sutcliffe, P., (2004) Topological Solitons, , Cambridge University Press
  • Moreno, E.F., Schaposnik, F.A., Dualities and bosonization of massless fermions in three dimensional space-time (2013) Phys. Rev. D, 88, p. 025033
  • Navarro-Lerida, F., Tchrakian, D.H., Non-Abelian Yang-Mills-Higgs vortices (2010) Phys. Rev. D, 81, p. 127702
  • Nielsen, H.B., Olesen, P., Vortex line models for dual strings (1973) Nuclear Phys. B, 61, pp. 45-61
  • Nolasco, M., Tarantello, G., On a sharp Sobolev-type inequality on two-dimensional compact manifolds (1998) Arch. Ration. Mech. Anal., 145, pp. 161-195
  • Nolasco, M., Tarantello, G., Vortex condensates for the SU(3) Chern-Simons theory (2000) Comm. Math. Phys., 213, pp. 599-639
  • Prasad, M.K., Sommerfield, C.M., Exact classical solutions for the 't Hooft monopole and the Julia-Zee dyon (1975) Phys. Rev. Lett., 35, pp. 760-762
  • Shifman, M., Yung, A., (2009) Supersymmetric Solitons, , Cambridge University Press, Cambridge, UK
  • Spruck, J., Yang, Y., Topological solutions in the self-dual Chern-Simons theory: existence and approximation (1995) Ann. Inst. H. Poincaré Anal. Non Linéaire, 12, pp. 75-97
  • Tarantello, G., Multiple condensate solutions for the Chern-Simons-Higgs theory (1996) J. Math. Phys., 37, pp. 3769-3796
  • Taubes, C.H., Arbitrary N vortex solutions to the first order Landau-Ginzburg equations (1980) Comm. Math. Phys., 72, pp. 277-292
  • Taubes, C.H., On the equivalence of the first and second order equations for gauge theories (1980) Comm. Math. Phys., 75, pp. 207-227
  • Wang, R., The existence of Chern-Simons vortices (1991) Comm. Math. Phys., 137, pp. 587-597
  • Wang, S., Yang, Y., Abrikosov's vortices in the critical coupling (1992) SIAM J. Math. Anal., 23, pp. 1125-1140
  • Yang, Y., The relativistic non-Abelian Chern-Simons equations (1997) Comm. Math. Phys., 186, pp. 199-218
  • Yang, Y., (2001) Solitons in Field Theory and Nonlinear Analysis, , Springer, New York

Citas:

---------- APA ----------
Chen, S., Han, X., Lozano, G. & Schaposnik, F.A. (2015) . Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor. Journal of Differential Equations, 259(6), 2458-2498.
http://dx.doi.org/10.1016/j.jde.2015.03.037
---------- CHICAGO ----------
Chen, S., Han, X., Lozano, G., Schaposnik, F.A. "Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor" . Journal of Differential Equations 259, no. 6 (2015) : 2458-2498.
http://dx.doi.org/10.1016/j.jde.2015.03.037
---------- MLA ----------
Chen, S., Han, X., Lozano, G., Schaposnik, F.A. "Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor" . Journal of Differential Equations, vol. 259, no. 6, 2015, pp. 2458-2498.
http://dx.doi.org/10.1016/j.jde.2015.03.037
---------- VANCOUVER ----------
Chen, S., Han, X., Lozano, G., Schaposnik, F.A. Existence theorems for non-Abelian Chern-Simons-Higgs vortices with flavor. J. Differ. Equ. 2015;259(6):2458-2498.
http://dx.doi.org/10.1016/j.jde.2015.03.037