Euclidean 4d exact solitons in a Skyrme type model

Abstract

We introduce a Skyrme type, four dimensional Euclidean field theory made of a triplet of scalar fields n, taking values on the sphere S^2, and an additional real scalar field phi, which is dynamical only on a three dimensional surface embedded in R^4. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory.

8 pages, 1 eps figure, plain latex, Comments on a possible connection with the low energy limit of pure SU(2) Yang-Mills theory are added. One reference added. Version accepted in Physics Letters B

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Cited by in corpus (3)

• Integrable theories and loop spaces: fundamentals, applications and new developments
• Gravitating Meron-like topological solitons in massive Yang-Mills theory and the Einstein-Skyrme model
• Self-dual Hopfions