Confinement of color and geometry

TL;DR

This paper explores the concept of confinement in gauge theories through symmetry, proposing that dual symmetry related to magnetic charge conservation explains confinement, and connects abelian and non-abelian Bianchi identities.

Contribution

It introduces a dual symmetry framework for confinement, linking magnetic charge conservation to non-abelian Bianchi identities in gauge theories.

Findings

Dual symmetry explains confinement in gauge theories.

Magnetic charge conservation relates to non-abelian Bianchi identities.

A set of abelian 't Hooft-like tensors characterizes the dual charge.

Abstract

A natural explanation of confinement can be given in terms of symmetry. Since color symmetry is exact, the candidate symmetry is dual and related to homotopy,i.e., in (3+1)d, to magnetic charge conservation. A set of r abelian 'tHooft-like tensors (r = rank of the gauge group) can be defined and the dual charge is a violation of the corresponding Bianchi identities. It is shown that this is equivalently described by non-abelian Bianchi identities.