Dual Description of Gauge Theories from an Iterative Noether Approach

TL;DR

This paper develops a dual description of gauge theories using an iterative Noether approach, connecting vector and tensor gauge fields without relying on gauge principles, and extends the framework to nonabelian symmetries.

Contribution

It introduces a novel dual formulation of gauge theories via an explicit map between vector and tensor fields, providing a minimal prescription and extending to nonabelian cases.

Findings

Established a duality between vector and tensor gauge fields.

Provided an explicit mapping connecting the two descriptions.

Extended the gauge invariance from abelian to nonabelian groups.

Abstract

An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic theories. No reference to any gauge principle, fractonic or otherwise, is required. A dual description is found where the theory is defined either in terms of the usual vector gauge field or, alternatively, in terms of higher derivatives of a symmetric tensor field. A connection between these two descriptions is obtained by providing an explicit map between the vector and tensor fields. This method yields a novel `minimal' prescription for the tensor fields which is identified with the usual minimal prescription for the vector fields by using the mapping. It also spells out the structure of the pure gauge field action in both formulations. Extension of the abelian $U(1)$ invariance to the nonabelian $SU(N)$ invariance is done for the standard formulation.