Large-N-approximated field theory for multipartite entanglement

We try to characterize the statistics of multipartite entanglement of the random states of an n-qubit system. Unable to solve the problem exactly we generalize it, replacing complex numbers with real vectors with Nc components (the original problem is recovered for Nc=2). Studying the leading diagrams in the large-Nc approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-Nc limit.