Large-N theory of strongly commensurate dirty-bosons: absence of transition in two dimensions

The spherical limit of strongly commensurate dirty-bosons is studied perturbatively at weak disorder and numerically at strong disorder in two dimensions (2D). We argue that disorder is not perfectly screened by interactions, and consequently that the ground state in the effective Anderson localisation problem always remains localised. As a result there is only a gapped Mott insulator phase in the theory. Comparisons with other studies and the parallel with disordered fermions in 2D are discussed. We conjecture that while for the physical cases N=2 (XY) and N=1 (Ising) the theory should have the ordered phase, it may not for N=3 (Heisenberg).