Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model

Details Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model

2001-05-17

arxiv.org/abs/math-ph/0105024v1

Physics

Mathematical Physics

30 pages including 11 embedded figures and 2 tables. Some of these results were previously reported in math-ph/9909015 and mat

Scientific paper

10.1088/0951-7715/15/2/301

We study singularity formation in spherically symmetric solutions of the charge-one and charge-two sector of the (2+1)-dimensional S^2 sigma-model and the (4+1)-dimensional Yang-Mills model, near the adiabatic limit. These equations are non-integrable, and so studies are performed numerically on rotationally symmetric solutions using an iterative finite differencing scheme that is numerically stable. We evaluate the accuracy of predictions made with the geodesic approximation. We find that the geodesic approximation is extremely accurate for the charge-two sigma-model and the Yang-Mills model, both of which exhibit fast blowup. The charge-one sigma-model exhibits slow blowup. There the geodesic approximation must be modified by applying an infrared cutoff that depends on initial conditions.

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