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

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## 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 constructed out of the gauge field with the gauge field itself. We specify the current through a set of defining equations. The explicit solution for the current is obtained in two spacetime dimensions and in the abelian case in three dimensions. The current can be viewed as arising from a non-local, gauge and Lorentz invariant mass term in three dimensions. We also construct 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 comment on the implications of this symmetry for \( \mathcal{N} = 1 \) supersymmetry.

## Keywords

Field Theories in Lower Dimensions Duality in Gauge Field Theories## References

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