Infinite reduction of couplings in non-renormalizable quantum field theory

I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the non-renormalizable terms as unique functions of a reduced set of independent couplings,, such that the divergences are removed by means of field redefinitions plus renormalization constants for the, lambda s. I consider nonrenormalizable theories whose renormalizable subsector R is interacting. The "infinite" reduction is determined by i) perturbative meromorphy around the free-field limit of R, or (ii) analyticity around the interacting fixed point of R. In general, prescriptions ( i) and ( ii) mutually exclude each other. When the reduction is formulated using ( i), the number of independent couplings remains finite or slowly grows together with the order of the expansion. The growth is slow in the sense that a reasonably small set of parameters is sufficient to make predictions up to very high orders. Instead, in case ( ii) the number of couplings generically remains finite. The infinite reduction is a tool to classify the non-renormalizable interactions and address the problem of their physical selection.