Branched polymers and dimensional reduction

Abstract

We establish an exact relation between self-avoiding branched polymers in $D+2$ continuum dimensions and the hard-core continuum gas at negative activity in $D$ dimensions. We review conjectures and results on critical exponents for $D+2 = 2,3,4$ and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in $D+2$ dimensions and the Yang-Lee edge singularity in $D$ dimensions.