Yangian symmetry for the tree amplituhedron

© 2017 IOP Publishing Ltd Printed in the UK. Tree-level scattering amplitudes in planar N = 4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows obtaining a general, explicit method to find such invariants. The uplifting of this result to the amplituhedron construction has been an important open problem. In this paper, with the help of methods proper to integrable theories, we successfully fill this gap and clarify the meaning of Yangian invariance for the tree-level amplituhedron. In particular, we construct amplituhedron volume forms from an underlying spin chain. As a by-product of this construction, we also propose a new on-shell diagrammatics for the amplituhedron.