Non-local symmetries for Yang-Mills theories and their massive counterparts in two and three dimensions

TL;DR

This paper discovers a non-local symmetry in Yang-Mills theories across 1+1 and 2+1 dimensions, revealing new algebraic structures and potential links to mass terms and supersymmetry.

Contribution

It identifies a novel non-local symmetry in low-dimensional Yang-Mills theories, including explicit solutions and algebraic structures, and explores its implications for mass generation and supersymmetry.

Findings

Explicit solutions for the current in 2D and 3D abelian cases.

The symmetry algebra contains an SO(2,1) subalgebra.

Evidence suggests the current arises from a non-local gauge-invariant mass term.

Abstract

We identify a non-local symmetry for Yang-Mills theories in 1+1 and 2+1 spacetime dimensions. The symmetry mixes a vector current with the gauge field. The current involved in the symmetry is required to satisfy certain constraints. The explicit solution for the current obeying these constraints, is obtained in two spacetime dimensions and in the abelian case in three dimensions. We conjecture that the current is generated from a non-local gauge and Lorentz invariant mass term in three dimensions and provide some evidence for it. We also posit a conserved current associated with the symmetry generators and derive some of its properties. In the Abelian case, we compute the symmetry algebra and show that additional symmetry generators have to be included for the algebra to close. The algebra contains an SO(2,1) subalgebra. We also comment on the implications of this symmetry for N=1 supersymmetry.