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

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.