On Abelian Multi-Chern-Simons Field Theories

TL;DR

This paper develops a new method to simplify multi-Chern-Simons field theories, enabling explicit calculation of partition functions for topologically linked polymers and clarifying previous ambiguities in the field.

Contribution

A general procedure is introduced to eliminate Chern-Simons fields, leading to explicit partition functions and resolving inconsistencies in models of linked polymers.

Findings

Derived explicit partition functions depending on topological numbers

Removed nonlocal terms from the action

Clarified ambiguities in topologically linked polymer models

Abstract

In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general procedure is presented to eliminate the Chern-Simons fields from their action. In this way it has been possible to derive an expression of the partition function of topologically linked polymers which depends explicitly on the topological numbers and does not have intractable nonlocal terms as it happened in previous approaches. The new formulation of multi-Chern-Simons field theories is then used to remove and clarify some inconsistencies and ambiguities which apparently affect field theoretical models of topologically linked polymers. Finally, the limit of disentangled polymers is discussed.