Fast Blow Up in the (4+1)-dimensional Yang Mills Model and the(2+1)-dimensional S^2 Sigma Model

Abstract

We study singularity formation in spherically symmetric solitons of the (4+1) dimensional Yang Mills model and the charge two sector of the (2+1) dimensional S^2 sigma model, also known as $\IC P^1$ wave maps, in the adiabatic limit. These two models are very similar. Studies are performed numerically on radially symmetric solutions using an iterative finite differencing scheme. Predictions for the evolution toward a singularity are made from an effective Lagrangian and confirmed numerically. In both models a characterization of the shape of a time slice f(r,T) with T fixed is provided, and ultimately yields an new approximate solutions to the differential equations that becomes exact in the adiabatic limit.