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We present a novel method to constrain the mass of ultra-light bosons as thedark matter using stellar streams formed by disrupting Globular Clusters in theMilky Way. The turbulent density field of Fuzzy Dark Matter (FDM) haloesresults in perturbations and dynamical heating of thin streams. Using numericalsimulations based on an effective model, we explore the magnitude of thisphenomenon and show that this is observable for the range of axion masses $m_a$that is interesting for alleviating the `small-scale problems' of $\Lambda$CDM.We derive an analytical model for the thickening of thin stellar streams andobtain an early conservative lower limit for the boson mass of $m_a > 1.5\times 10^{-22}~$eV, using pre-Gaia literature data for six Milky Way streamsand after marginalizing over physical parameters. This demonstrates the greatpromise for using this novel dynamical method as a fully independent probe ofFDM, to complement results based on Lyman-$\alpha$ forest data.

First constraints on Fuzzy Dark Matter from the dynamics of stellar streams in the Milky Way