Self-Avoiding Walks with Writhe

TL;DR

This paper explores the effects of writhe on self-avoiding walks by mapping them to a complex Chern-Simons theory, finding that small writhe potential is irrelevant while large potential causes polymer collapse.

Contribution

It introduces a theoretical mapping of self-avoiding walks with writhe to Chern-Simons theory and analyzes the impact of writhe chemical potential on polymer behavior.

Findings

Small writhe chemical potential is irrelevant at the fixed point.

Chern-Simons field does not alter monomer correlations for small potential.

Large writhe potential induces polymer collapse.

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 nu = 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.