Shift symmetries and duality web in gauge theories

TL;DR

This paper develops a comprehensive framework using a generalized Noether approach to analyze shift symmetries, revealing dualities and connections among gauge theories with vector and tensor fields, including applications to fracton models.

Contribution

It introduces a unified scheme for deriving currents and conservation laws in shift symmetric theories and establishes duality maps linking vector and tensor gauge descriptions.

Findings

Identifies identities among matter sector currents that underpin duality.

Demonstrates how to couple shift symmetric theories to gauge fields via a modified minimal prescription.

Establishes duality relations connecting different gauge field descriptions and classical laws.

Abstract

Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the basis for revealing a dual picture when the full interacting theory is considered by coupling to gauge fields. The coupling is achieved in terms of vector fields by adhering to a modified minimal prescription which is also supported by an iterative Noether scheme. Further, this scheme shows that couplings can also be introduced using higher rank tensor gauge fields that have appeared in recent discussions on fractons. We reveal a connection among these descriptions (using vector or tensor fields) through certain duality maps that relate the various fields (gauge, electric and magnetic) in the two cases. A correspondence is established among the Gauss' law, Faraday's law and Ampere's law. Explicit calculations are provided for linear and quadratic shift symmetric lagrangians.