Possible Constraints on String Theory in Closed Space with Symmetries

TL;DR

This paper reviews quadratic constraints in linearized gravity on symmetric closed spaces and highlights the absence of a necessary mode in free bosonic string spectra, questioning certain theoretical assumptions.

Contribution

It identifies a missing mode in string spectra that challenges the applicability of gravity constraints in closed symmetric spaces.

Findings

Negative kinetic energy mode is absent in string spectrum.

Constraints in linearized gravity relate to mode presence.

Implications for string theory in closed spaces.

Abstract

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.