Symmetries and the Hilbert Space of Large N Extended States

We discuss the large N expansion in backgrounds of extended states with a focus on the implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. The case of translational symmetry is described first as a basic example. The large N thermofield represents the main topics, with the emergent dynamics of left–right bulk fields and collective symmetry coordinates. These give the basis for a 1/N expansion.