Topological Constraints at the Theta Point: Closed Loops at Two Loops

TL;DR

This paper models topologically constrained polymers at the Theta point using a U(N)-Chern-Simons theory, revealing a new scaling regime with exponents influenced by writhe and a transition driven by fluctuations.

Contribution

It introduces a novel field-theoretic approach to describe topologically constrained polymers, connecting polymer physics with gauge theory and uncovering new critical behavior.

Findings

Identification of a new scaling regime for topologically constrained polymers.

Critical exponents depend on the chemical potential for writhe.

Discovery of a fluctuation-induced first-order transition.

Abstract

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 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.