Polymers and Topological Field Theory: A 2 Loop Computation

TL;DR

This paper demonstrates the perturbative renormalizability of a topological polymer model using the Quantum Action Principle and performs a two-loop computation revealing its predictive power and phase structure.

Contribution

It establishes the renormalizability of a topological polymer theory and provides a detailed two-loop analysis showing its phase behavior and comparison to De Gennes theory.

Findings

The theory is perturbatively renormalizable.

It has the same predictive power as De Gennes theory.

The theory exhibits two distinct phases.

Abstract

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.