Abstract
We show that magnons in two-dimensional altermagnets can spontaneously decay at zero temperature. The decay rate is determined by quantum fluctuations and scattering processes involving the decay of a single magnon into three. These processes are kinematically allowed due to the convexity of the altermagnetic magnon dispersion. For small wavevectors k the decay rate is proportional to k⁵ with a direction-dependent prefactor which is maximal along the diagonals of the Brillouin zone. Moreover, for a given momentum only magnons with one specific chirality can spontaneously decay.