= Sigma-model lump
{title2=$E=4\pi|N|$}
A sigma-model lump is a finite-energy <classical field-theory soliton> of the two-dimensional <O3 nonlinear sigma model>. With an orientation chosen so holomorphic maps have positive charge, the <Bogomolny bound> $E\geq4\pi|N|$ is saturated by <rational maps> of degree $N>0$ in a <stereographic projection> coordinate, and by antiholomorphic maps for negative charge. The field remains smooth at coordinate poles, which are points at the other pole of the target sphere. Scale invariance permits lumps of arbitrary size; topology alone does not prevent concentration to a singular limiting configuration.
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