Self-avoiding walks with writhe

Abstract

We map self-avoiding random walks with a chemical potential for writhe to the three-dimensional complex O( N) Chern-Simons theory as N → 0. We argue that at the Wilson-Fisher fixed point which characterizes normal self-avoiding walks (with radius of gyration exponent β ≈ 0.588) a small chemical potential for writhe is irrelevant and the Chern-Simons field does not modify the monomer-monomer correlation function. For a large chemical potential the polymer collapses.