Topological constraints at the Theta-point: Closed loops at two loops

We map the problem of self-avoiding random walks in a Θ solvent with a chemical potential for writhe to the three-dimensional symmetric $U(N)$-Chern-Simons theory as $N\rightarrow 0$. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe which gives way to a fluctuation-induced first-order transition.