Supersymmetric form of the nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>model in two dimensions

A supersymmetric form of the two-dimensional nonlinear $\ensuremath{\sigma}$ model is described; the primary purpose is to explore further the analogy between the $\ensuremath{\sigma}$ model and four-dimensional Yang-Mills theory. In the case of three components, the theory contains an enlarged supersymmetry algebra and is equivalent to the ordinary $\ensuremath{\sigma}$ model with an additional logarithmic interaction between pseudoparticles.