Critical behaviour of directed branched polymers and the dynamics at the Yang-Lee edge singularity

Relying on a field theoretic model due to Day and Lubensky we establish the one-to-one correspondence of the directed branched polymer problem ind dimensions to (relaxational) critical dynamics at the Yang-Lee edge ind–1 spatial dimensions; like their isotropic counterparts the directed polymer exponents andv are uniquely determined by the static Yang-Lee exponent whereasv requires in addition the dynamic Yang-Lee exponentz. JoiningO(²)-expansions about the upper critical dimensiond_c=7 to exact results atd=1 and 2 by Padé-interpolations we obtain good agreement with series expansion data for low dimensions.