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Whilst standard field theoretic Cosmic Strings cannot end, Cosmic Superstrings can form three string junctions, at which each string ends. This opens up a new class of possible boundary conditions for such strings and we show that, at least when the junctions are close together, a string ending of two such junctions will generically have cusps. Cusps are of particular interest as they are strong emitters of radiation (both gravitational and particle) and hence are possible observables. The detection of cusps from Cosmic Superstrings between junctions would be a rare observational window into the realm of String theory and Brane inflation models.

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