Volume 196, number 4 PHYSICS LETTERSB 15 October 1987 FINITE-ENERGY SU(3) MONOPOLES * J. KUNZ ~ and D. MASAK Institut fiir Theoretische Physik, Universitiit Giessen, D-6300 Giessen, Fed. Rep. Germany Received 17 July 1987 Classical SU(3) Yang-Mills-Higgstheory with the Higgsfield in the adjoint representation is studied, when the SU(3) sym- metry is broken down to U(2) and U (1) × U (1). Sphericallysymmetric equations of motion are solved for various boundary conditions. The finite-energy solutions correspondto magneticmonopolesand isopoles. 1. Introduction 't Hooft [ 1 ] and Polyakov [ 2 ] observed that the classical SU (2) gauge theory, where the SU (2) sym- metry is broken down to U(1 ) by a triplet of Higgs fields [3], possesses a regular finite-energy soliton solution with conserved topological charge. Regard- ing the unbroken U(1 ) group as the electromagnetic gauge group, the topological charge corresponds to the magnetic charge. The soliton represents a mag- netic monopole. The physical interest in such monopoles is mani- fold; it ranges from the prediction of new particle- like objects to the possible relevance of monopoles to colour confinement in QCD. The 't Hooft-Polyakov monopole, dyons and monopoles with multiple magnetic charge have been studied extensively [4,5] in SU(2) gauge theory as well as the embedding of the SU(2) solutions in higher gauge groups SU(N). For such groups beyond SU(2), however, new features arise [6]. There are different ways to break down the SU(N) gauge symmetry by a Higgs multiplet in the adjoint representation. Fur- ther, there are various possible asymptotic field con- figurations, that can be classified by charges representing the unbroken subgroups. The 't Hooft-Polyakov monopole has another remarkable property. It possesses a generalized spherical symmetry, i.e., the field satisfy ~r Work supported by DFG under contract Ku612/1-1, BMFT and GSI Darmstadt. Address after August 1 ~, 1987: NIKHEF-K, P.O. Box 41882, NL-1009 DB Amsterdam, The Netherlands. [Li+Ti, Aj] =ieijkAk, [Li+Ti, qb] = 0 , (1) where Ti are the group generators and L = -r× V. In the more general case of spherically symmetric SU(N) monopoles, the Ti generate some SU(2) or SO (3) subgroup. The possible spherically symmetric asymptotic field configurations were constructed for SU(3) [ 6 ] and higher groups [7,8]. They represent infinite- energy point monopoles and isopoles, singular at the origin. To obtain finite-energy solutions, this sin- gularity must be smoothed out by radial functions, subject to certain boundary conditions at the origin. Beside the generalizations [9] of the 't Hooft-Polyakov monopole there is only one regular finite-energy solution known for SU(3) [ 10,11 ] [SU(N)]. In addition, the existence of another reg- ular finite energy SU (3) monopole was shown [ 12 ]. Here we consider the spherically symmetric SU(3) monopoles [6,9]. We construct the possible finite- energy solutions, e.g. the predicted monopole [ 12]. Some solutions with distinct boundary conditions are related by singular gauge transformations. We study the dependence of the solutions on the Higgs poten- tial parameters. 2. Model We study the SU (3) gauge theory with an octet of Higgs fields given by the lagrangian ~= 1 2 - ~TrFu, - ]TrDu • 2 - V(q~), (2) where 0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 513