Possible Constraints on String Theory in Closed Space with Symmetries
  It is well known that certain quadratic constraints have to be imposed on linearized gravity in closed space with symmetries. We review this phenomenon and discuss one of the constraints which arise in linearized gravity on static flat torus in detail. Then we point out that the mode with negative kinetic energy, which is necessary for satisfying this constraint, appears to be missing in the free bosonic string spectrum. 
Atsushi Higuchi