Factorization and non-factorization of in-medium four-quark condensates

It is well-established for the vacuum case that in the limit of a large number of colors Nc the four-quark condensates factorize into products of the two-quark condensate. It is shown that in the combined large-Nc and linear-density approximation four-quark condensates do not factorize in a medium of pions (finite-temperature system) but do factorize in a medium of nucleons (nuclear system).