String theory and the classical stability of plane waves

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 world sheet scalars with such tachyonlike 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 world sheet scalars with negative mass-squared. We argue that this background is perturbatively stable.