Field theory of self-avoiding walks in random media

Based on the analogy with the quantum mechanics of a particle propagating i n a complex potential, we develop a field-theoretical description of the st atistical properties of a self-avoiding polymer chain in a random environme nt. We show that the account of the non-Hermiticity of the quantum Hamilton ian results in a qualitatively different structure of the effective action, compared to previous studies. Applying renormalization group analysis, we find a transition between the weak-disorder regime, where the quenched rand omness is irrelevant, and the strong-disorder regime, where the polymer cha in collapses. However, the fact that the renormalized interaction constants and the chiral symmetry breaking regularization parameter flow towards str ong coupling raises questions about the applicability of the perturbative a nalysis.