Randomly branched polymers and conformal invariance

Jeffrey D. Miller; Keith De'Bell

doi:doi:10.1051/jp1:1993211

Numéro		J. Phys. I France Volume 3, Numéro 8, August 1993


Page(s)		1717 - 1728
DOI		https://doi.org/10.1051/jp1:1993211

DOI: 10.1051/jp1:1993211
J. Phys. I France 3 (1993) 1717-1728

Randomly branched polymers and conformal invariance

Jeffrey D. Miller¹ and Keith De'Bell²

¹ Service de Physique Théorique de Saclay, 91191 Gif-sur-Yvette Cedex, France
² Trent University, Department of Physics, Peterborough, Ontario K9J 7B8 Canada

(Received 1 December 1992, revised 3 March 1993, accepted 27 April 1993)

Abstract
We show that the field theory that describes randomly branched polymers does not have the structure one expects of a two-dimensional conformal field theory. In particular, we show that the lowest dimension operator in the theory cannot be primary. We show moreover that the free field theory obtained by setting the potential equal to zero in the branched polymer theory is not even classically conformally invariant. Finally, we present numerical data for the exponent $\theta(\alpha)$ , defined by $T_N(\alpha) \sim \lambda^N N^{-\theta(\alpha)+1}$ , where $T_N(\alpha)$ is number of distinct configurations of a branched polymer rooted near the apex of a cone with apex angle $\alpha$ . The data indicate that $\theta(\alpha)$ is not linear in $1/\alpha$ , providing further evidence that correlation functions which generate randomly branched polymers do not transform simply under conformal transformations.