Mass spectrum and correlation functions of non-Abelian quantum magnetic monopoles.

The method of quantization of magnetic monopoles based on the order-disorder duality existing between the monopole operator and the lagrangian fields is applied to the description of the quantum magnetic monopoles of ‘t Hooft and Polyakov in the SO(3) Georgi-Glashow model. The commutator of the monopole operator with the magnetic charge is computed explicitly, indicating that indeed the quantum monopole carries 4π/g units of magnetic charge. An explicit expression for the asymptotic behavior of the monopole correlation function is derived. From this, the mass of the quantum monopole is obtained. The tree-level result for the quantum monopole mass is shown to satisfy the Bogomolnyi bound (Mmon ≥ 4πMg2 ) and to be within the range of values found for the energy of the classical monopole solution. On sabbatical leave from Departamento de F́ısica, Pontif́ıcia Universidade Católica, Rio de Janeiro, Brazil. E-mail: [email protected] E-mail: [email protected] 1) Introduction A few years ago a general method of quantization of nonabelian magnetic monopoles was established [1] by exploiting the general fact that the operator which creates the topological excitations of a certain theory must also be dual to the basic lagrangian fields (in the sense of order-disorder duality) [2]. This method of quantization has been applied to a variety of systems containing topological excitations in two, three and four dimensional spacetime [3, 4, 5]. The nonabelian monopoles are topological excitations which occur when a nonabelian symmetry group (with compact covering) of a gauge theory is spontaneously broken down to a U(1) symmetry. The topological charge of the monopoles is the abelian magnetic charge corresponding to the unbroken U(1) [6]. As a consequence of the fact that monopoles are topological excitations appearing in a process of symmetry breakdown, it can be shown [1, 2] that for groups with a compact covering, the quantum creation operator of magnetic monopoles is the disorder variable for the phase transition in which the Higgs field develops a vacuum expectation value and thereby generates a mass to the gauge fields. In a Higgs phase, where 〈φ〉 6 = 0, we must have the vacuum expectation value of the monopole operator (μ operator) 〈μ〉 = 0. This automatically implies that μ creates states which are orthogonal to the vacuum, i.e., nontrivial states [2]. An explicit expression for the monopole operator in terms of the basic lagrangian fields of the theory is then constructed by imposing that it must satisfy an order-disorder algebra with these fields. Also a general expression for the correlation functions of these operators is obtained as an euclidean functional integral over the lagrangian fields by generalizing the methods first introduced by Kadanoff and Ceva for the description of correlation functions of disorder variables in the Ising model [8]. In the present work, we consider the magnetic monopoles of the SO(3) Georgi-Glashow model. We take the expression obtained in [1] for the quantum operator corresponding to the classical monopole solution and evaluate the long distance behavior of its two point correlation function by using the functional integral methods developed in [1]. We show that this correlation function decays exponentially and from its explicit expression the mass