The n = 0 replica limit of U(n) and U(n)/SO(n) models

Recently the replica limit n = 0 of the U(n) and U(n)/SO(n) models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and U(n)/SO(n). This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and U(n)/SO(n) and draw consequences for these functions in this limit.