We would like to show in this paper that there exist a whole range of screening solutions of multirnonopole by unit charge antimonopoles in the SU(2) Yang-Mills-Higgs theory

Teh, Rosy

Wong, Khai Ming

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SCREENING SOLUTIONS OF MULTIMONOPOLE BYUNIT CHARGE ANTIMONOPOLES*Rosy Teht and Khai-Ming WongtSchOQl of Physics; Universiti Sains Malaysia; 11800 USMPenang; Malysia.ABSTRACTWe would like to. show in this paper that there exist a whole range of screening solutions ofmultirnonopole by unit charge antimonopoles in the SU(2) Yang-Mills-Higgs theory. These screeningsolutions are exact multimonopole-antimonopoles configurations, wh the positively charged'multimonQpole is screened by unit charged antimonopoles located or ;;;Zgb " ·~,;th themultirnonopole positioned at the center of the spherical shell. These solunUll.:l u__ _,~ 'I-Bogomol'nyi equation but possess infinite energy. Hence they are a different type of BPS solutlOn~. ~ h_these screening solutions possess rotational symmetry about the z-axis.INTRODUCTIONThe SU(2) Yang.,Mills-Higgs (YMH) theory, with the Higgs field in the adjoint representation,possesses both the magnetic monopole and multimonopole solutions [1, 2, 3]. The simplest solutionwith unit magnetic charge is the spherically symmetric 't Hooft-Polyakov monopole [1].Multimonopole solutions cannot be spherically symmetric and possess at most axial symmetry [3]. Inparticular, there are no solutions ofmagnetic charge greater than one with .radiaf symmetry. Analyticmonopole and multimonopole solutions [1, 2, 3] have been shown to exist in the Bogomol'nyi-Prasad-Sommerfield (BPS) limit with vanishing Higgs potential. These solutions satisfy the first orderBogomol'nyiequations and they have minimal energies. However, when the Higgs potential is [mite,there exist only numerical monopole and multimonopole solutions [3].Recently, axially symmetric monopoles-antimonopoles chain solutions which do not satisfythe' Bogomol'nyi condition were constructed numerically. These non-Bogomol'nyi solutions exist. both in the .limit of a vanishing Higgs potential as well as in the presence of a finite Higgs potential.BPS axially symme.tric vortex rings solutions have also been constructed numerically [4].We would like to show in this paper there exist a whole range screening solutions by unitcharge antimonopoles in the SU(2) YMH model. These screening solutions were actually frrstreported in ref. [5] and they were labeled as the Al and the B1 solutions. The screening solutions areexact multimonopole-antimonopoles configurations where the positively charged multimonopole isscreened by unit charged antimonopoles located on a spherical shell, with the multimonopolepositioned at the center of the shell. The SU(2) YMH model in our. work is of vanishing Higgspotential. The solutions are solved from the second order Euler-Lagrange equations and the fITst orderBogomol'nyi equations Bt ±D/PQ = 0 with the positive sign. The screening solutions satisfy the frrstorder Bogomol'nyi equation but possess infinite energy. Hence they are a different type of BPSsolutions.'.. USM Preprint August 2004; Contributed paper presented at the "Persidangan Fizik Kebangsaan", (PERFIK 04), October5-7, 2004, Palace of the Golden Horses, Kuala Lumpur.t e-mail: rosyteh@usm.my~ Speaker; e-mail: khairningl@hotmail.com1

Screening Solutions Of Multimonopole By Unit Charge Antimonopoles.

http://eprints.usm.my/11465/1/Screening_Solutions_of_Multimonopole_by_Unit_(PPSFizik)_2005.pdf

Screening Solutions Of Multimonopole By Unit Charge Antimonopoles.

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