I'm reading Alvarez-Gaume review on Seiberg-Witten theory: http://arxiv.org/abs/hep-th/9701069.
Around page 23 you can find the following claim:
"This is a Clifford algebra with 2N generators and has a 2N-dimensional representation. From the point of view of the angular momentum algebra, a^I...
Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...