  We propose a new constraint on the structure of strongly coupled field
theories. The constraint takes the form of an inequality limiting the number of
degrees of freedom in the infrared description of a theory relative to the
number of underlying, ultraviolet degrees of freedom. We apply the inequality
to a variety of theories (both supersymmetric and nonsupersymmetric), where it
agrees with all known results and leads to interesting new constraints on low
energy spectra. We discuss the relation of this constraint to Renormalization
Group c-theorems.
