Towards Abelian-like formulation of the dual gluodynamics

TL;DR

This paper explores a dual gluodynamics framework incorporating both color and magnetic charges, demonstrating Abelian interactions at short distances and proposing an effective model that preserves Casimir scaling.

Contribution

It introduces an Abelian-like formulation of dual gluodynamics that accounts for monopoles with different charges and their interactions, extending previous models.

Findings

External monopoles interact as pure Abelian objects at short distances.

A Zwanziger-type Lagrangian reproduces Abelian interactions.

Proposed effective dual gluodynamics model maintains Casimir scaling.

Abstract

We consider gluodynamics in case when both color and magnetic charges are present. We discuss first short distance physics, where only the fundamental |Q|=1 monopoles introduced via the `t Hooft loop can be considered consistently. We show that at short distances the external monopoles interact as pure Abelian objects. This result can be reproduced by a Zwanziger-type Lagrangian with an Abelian dual gluon. We introduce also an effective dual gluodynamics which might be a valid approximation at distances where the monopoles |Q|=2 can be considered as point-like as well. Assuming the monopole condensation we arrive at a model which is reminiscent in some respect of the Abelian Higgs model but, unlike the latter leaves space for the Casimir scaling.