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We argue that the field theory that descibes randomly branched polymers is not generally conformally invariant in two dimensions at its critical point. In particular, we show (i) that the most natural formulation of conformal invariance for randomly branched polymers leads to inconsistencies; (ii) that the free field theory obtained by setting the potential equal to zero in the branched polymer field theory is not even classically conformally invariant; and (iii) that numerical enumerations ofdoi:10.1051/jp1:1993211 fatcat:srix4kcfj5emzdwbxvwl3urbxm