We establish an exact isomorphism between self-avoiding branched
polymers in D+2 continuum dimensions and the hard-core continuum
gas at negative activity. 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.
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