Shift symmetries and duality web in gauge theories. (English) Zbl 1535.81243
Summary: 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.
MSC:
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 14H51 | Special divisors on curves (gonality, Brill-Noether theory) |
| 37K06 | General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 81T32 | Matrix models and tensor models for quantum field theory |
| 08C20 | Natural dualities for classes of algebras |
| 18D60 | Profunctors (= correspondences, distributors, modules) |
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