Monopole solutions in classical SU(3) gauge theory
Abstract
We consider monopole solutions in nonabelian SU(3) Yang – Mills – Higgs gauge theory. Using spherically symmetric ansatz for SU(3) gauge and scalar fields, we obtain Yang – Mills – Higgs equations as well as Bogomol’nyi equations. We show that statically Yang – Mills – Higgs equations follow from Bogomol’nyi equations. Bogomol’nyi equation system comprising four first-order differential equations was transformed into the system consisting of two second-order differential equations, and two algebraic equations. By Taylor-expanding equations, we obtain approximate analytical solutions at the centre of the monopole. We also consider asymptotic behavior of the monopole solutions. Complete solution is obtained numerically. We show that the monopole solutions depend on two parameters, and we obtain the dependence of the energy of the monopole on these parameters. On the parameters plane we obtain a curve that separates regular and singular solutions.
References
2. ‘t Hooft, G. Magnetic monopoles in unified gauge theories // Nuclear Physics B. – 1974. – Vol. 79. – P. 276-284.
3. Polyakov A.M. Spektr chastits v kvantovoi teorii polya // Pis’ma v ZhETF. – 1974. – Vol. 20. - № 6. – P. 430-433. (in Russ)
4. Prasad M.K., Sommerfield C.M. // Phys. Rev. Lett. – 1975. – 35. – C. 760; Bogomol’nyi Ye.B. // Yadernaya Fizika. – 1976. – Vol. 24. – P. 449. (in Russ)
5. Lee Ki-Myeong, Weinberg E.J., Yi Piljin. Electromagnetic duality and SU(3) monopoles. Phys.Lett. – 1996. – Vol. B376. – P. 97-102.
6. Rosy Teh, Khai-Ming Wong. // J. Math. Phys. – 2005. – Vol. 46. – P. 082301; Int. J.Mod. Phys. – 2005. – Vol. A20. – P. 4291.
7. Kleihaus B., Kunz, J. Shnir, Y. Monopole-Antimonopole Chains and Vortex Rings // arXiv:hep-th/0405169. – 2004.
8. Sethi S., Stern S., Zaslow E. // Nucl. Phys. – 1995. – Vol. B457. – P. 484; Gauntlett, J.P., Harvey, J. S-Duality and the Dyon Spectrum in N=2 Super Yang-Mills Theory. // arXiv:hep-th/9508156. – 1995.
9. Rosy Teh, Ban-Loong Ng, Khai-Ming Wong. Electrically Charged One and a Half Monopole Solution // arXiv:hep-th/1312.6483. – 2013.
10. Rosy Teh, Ban-Loong Ng, Khai-Ming Wong. The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory // Annals of Physics – 2014. – Vol. 343. – P. 1-15.
11. Sardanashvili, G.A. Sovremennyie metody teorii polya. 1. Geometriya i klassicheskiye polya. – 2nd edition. – M.: URSS, 2011. (in Russ)
12. Gal’tsov, D.V., Grats, Yu.V., Zhukovskii, V.Ch. klassicheskiye polya. – M.: MGU, 1991. (in Russ)
13. Horvath, Z., Palla, L. Dyons in classical SU(3) gauge theory and a new topologically conserved quantity // Phys. Rev. – 1976. – Vol. D14. – P. 1711.
14. Baltsov, D.V., Volkov, M.S. Phys.Lett. – 1990. – Vol. B274. – P. 173.
15. Irwin, P. SU(3) monopoles and their fields // Phys.Rev. – 1997. – Vol. D56. – С. 5200-5208.
16. Dzhunushaliev, V.D., Singleton, D. Confining solutions of SU(3) Yang-Mills theory. // arXiv:hep-th/9902076. – 1999.
17. Shnir, Y. Magnetic monopoles. – Springer-Verlag, Berlin, 2005 (ISBN 3540252770).
