Unparticle actions and gauge invariance

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We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which create gauge invariant coloured unparticles. We discuss both their perturbative and non--perturbative properties.
15 pages. V2: references added. Version to appear in PRD

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