Randomly branched polymers and conformal invariance

Jeffrey D. Miller, Keith De'Bell
1993 Journal de Physique I  
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 of
more » ... he exponent θ (α ), defined by T_N(α )∼λ^NN^-θ (α ) +1, where T_N(α ) is number of distinct configuratations of a branched polymer rooted near the apex of a cone with apex angel α, indicate that θ (α ) is not linear in 1/α contrary to what conformal invariance leads one to expect.
doi:10.1051/jp1:1993211 fatcat:srix4kcfj5emzdwbxvwl3urbxm