Supersymmetric Strings on Grassmann Manifolds

One of the fundamental problems in string theory is understanding the geometry of the underlying space or 'target space' on which the string dynamics are formulated. In conventional string theory, attempts are made to identify this initially undetermined space via consistency and phenomenological arguments. A new string model and its supersymmetric generalization are proposed in which the world-sheet coordinates of the string represent the Stiefel coordinates of a Grassmann Manifold, Gk, the set of all k-dimensional linear subspaces of the embedding space. In this formulation the intrinsic geometry of the model is made manifest in the initial formulation of the Lagrangian.