Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain

TL;DR

This paper explores a generalized elastic chain model that includes topological and non-topological fields, showing how the non-topological field acts as an auxiliary in the sine-Gordon limit, with implications for broader field theories.

Contribution

It introduces a perturbative framework for understanding how non-topological fields can be auxiliary in sine-Gordon-like models, extending previous DNA chain studies.

Findings

Non-topological fields can be treated as auxiliary fields in the sine-Gordon limit.

The model generalizes previous DNA chain dynamics to a broader class of field theories.

The framework predicts auxiliary behavior in a wide range of similar models.

Abstract

We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of field-theoretical models.