Sigma model
In physics, a sigma model is a physical system that is described by a Lagrangian density of the form:
Depending on the scalars in gij, it is either a linear sigma model or a non-linear sigma model. The fields φi, in general, provide a map from a base manifold called the worldsheet to a target (Riemannian) manifold of the scalars linked together by internal symmetries. (In string theory, however, that is often understood to be the actual spacetime.)