  The presence of fields with negative mass-squared typically leads to some
form of instability in standard field theories. The observation that, at least
in the light-cone gauge, strings propagating in plane wave spacetimes can have
worldsheet scalars with such tachyon-like masses suggests that the supergravity
background may itself be unstable. To address this issue, we perform a
perturbative analysis around the type IIB vacuum plane wave, the solution which
most obviously generates worldsheet scalars with negative mass-squared. We
argue that this background is perturbatively stable.
