Gauging dual symmetry

TL;DR

This paper explores reversing the traditional gauge process by gauging electric-magnetic dual symmetry, revealing that matter fields must be introduced and roles of fields are interchanged, offering new insights into gauge theories.

Contribution

It demonstrates that gauging electric-magnetic dual symmetry necessitates matter fields and reverses the usual roles of vector and matter fields in gauge theories.

Findings

Gauging dual symmetry requires matter fields.

Roles of vector and matter fields are interchanged.

Provides a new perspective on gauge symmetry principles.

Abstract

The idea of gauging (i.e. making local) symmetries of a physical system is a central feature of many modern field theories. Usually, one starts with a Lagrangian for some scalar or spinor matter fields, with the Lagrangian being invariant under a global phase symmetry transformation of the matter fields. Making this global phase symmetry local results in the introduction of vector fields. The vector fields can be said to arise as a result of the gauge principle. Here we show that this chain of reasoning can be reversed: by gauging the electric-magnetic dual symmetry of a Lagrangian which originally contains only the vector gauge fields we find that it is necessary to introduce matter fields (scalar fields in our example). In this gauging of the electric-magnetic dual symmetry the traditional roles of the vector fields and the matter fields are interchanged.