 String-frame massless effective action

The leading massless-sector spacetime action is proportional to $\int \sqrt{-G}{e}^{-2\Phi }[R+4(\nabla \Phi {)}^2-H^2/12]$, with $H=dB$. The backgrounds are the string-frame metric, dilaton, and Kalb–Ramond field. Massive string exchange generates higher-derivative corrections ordered by ${\alpha }^{\prime }$. This perturbative bosonic massless-sector truncation does not remove the tachyon instability.