  The graviton S-matrix has a famous soft pole. We show that the S-matrix for
cylindrical gravitational waves has a soft zero. The soft pole for ordinary
gravitons comes from a Ward identity for supertranslation symmetry at
asymptotic infinity. We show that the soft zero for cylindrical gravitational
waves comes from a Ward identity for Geroch symmetry at asymptotic infinity.
Because it is a zero rather than a pole, there is no memory effect. Overall,
this soft zero is a manifestation of Geroch symmetry and of the extraordinary
simplicity of cylindrical gravitational waves.
