Polymers and Topological Field Theory: A 2 Loop Computation

Within the Quantum Action Principle framework we show the perturbative renormalizability of previously proposed topological lagrangian \`a la Witten-Fujikawa describing polymers, then we perform a 2 loop computation. The theory turns out to have the same predictive power of De Gennes theory, even though its running coupling constants exhibit a very peculiar behaviour. Moreover we argue that the theory presents two phases , a topological and a non topological one.