  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.
