Abstract
Motivated by the problem of N-coupled Hubbard chains, we investigate a generalization of a recent model containing two species of one-dimensional fermions interacting via a gauge field that depends on the positions of all the particles of the other species. The exact many-body ground state of the model can be easily obtained through a unitary transformation of the model. The correlation functions are Luttinger like - i.e., they decay through power laws with non-integer exponents. Through the interaction-dependent two-particle correlation functions, we identify the relevant perturbations and hence, possible instabilities. Interestingly, for N>2 bands, beyond a critical strength of the interaction, the dominant incipient instability changes.