The collapse transition of randomly branched polymers -renormalized field theory

We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well established dimensional-reduction results from a different angle. For the collapse $\theta$-transition, we uncover a hidden Becchi-Rouet-Stora super-symmetry, signaling the sole relevance of tree-configurations. We correct the long-standing 1-loop results for the critical exponents, and we push these results on to 2-loop order. For the collapse $\theta^{\prime}$-transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions.