We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Mathematical Sciences


Publication details for Professor Emeritus Wojtek Zakrzewski

Ferreira, L.A. & Zakrzewski, W.J. (2013). A Skyrme-like model with an exact BPS bound. Journal of High Energy Physics 2013(9): 097.

Author(s) from Durham


We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three-dimensional space R3R3 . We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.