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The Vega planetary system hosts the archetype of extrasolar Kuiper belts and is rich in dust from the sub-astronomical unit region out to hundreds of astronomical units, suggesting intense dynamical activity. We present Atacama Large Millimeter/submillimeter Array (ALMA) millimeter observations that detect and resolve the outer dust belt from the star for the first time. The interferometric visibilities show that the belt can be fit by a Gaussian model or by power-law models with a steep inner edge (at 60–80 au). The belt is very broad, extending out to at least 150–200 au. We strongly detect the star and set a stringent upper limit to warm dust emission previously detected in the infrared. We discuss three scenarios that could explain the architecture of Vega's planetary system, including the new ALMA constraints: no outer planets, a chain of low-mass planets, and a single giant planet. The planetless scenario is only feasible if the outer belt was born with the observed sharp inner edge. If, instead, the inner edge is currently being truncated by a planet, then the planet must be and at to have cleared its chaotic zone within the system age. In the planet chain scenario, outward planet migration and inward scattering of planetesimals could produce the hot and warm dust observed in the inner regions of the system. In the single giant planet scenario, an asteroid belt could be responsible for the warm dust, and mean motion resonances with the planet could put asteroids on star-grazing orbits, producing the hot dust. [ABSTRACT FROM AUTHOR]