JACOBI ELLIPTIC MONOPOLE–ANTIMONOPOLE PAIR SOLUTIONS

Abstract

We present new classical generalized Jacobi elliptic one monopole–antimonopole pair (MAP) solutions of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with θ-winding number m = 1 and ϕ-winding number n = 1, 2, 3,…,6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behavior of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing (λ = 0) and nonvanishing (λ = 1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the 1-MAP solution with winding number m = 1. However these total energies are significantly lower than the total energy of the 1-MAP solution with winding number m = 2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang–Mills–Higgs field theory.