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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.

The string nonlinear sigma model couples the worldsheet embedding fields to target-space backgrounds such as a metric, a Kalb–Ramond field and a dilaton. Quantum Weyl invariance requires its beta functions to vanish.

An antisymmetric tensor potential $B$ has gauge transformation $B\mapsto B+d\alpha$, where $\alpha$ is a one-form. Its field strength is the three-form $H=dB$, invariant because $d^2=0$. The Kalb–Ramond field is the string-theory example.

Massless type IIA supergravity is the nonchiral ten-dimensional maximal supergravity with metric, Kalb–Ramond field, dilaton, Ramond-Ramond one-form and three-form potentials, two opposite-chirality Majorana-Weyl gravitini, and two opposite-chirality Majorana-Weyl dilatini. Its massless spectrum has $128$ bosonic and $128$ fermionic polarizations. The two supercharges have opposite ten-dimensional chirality.

Type IIB supergravity is the chiral ten-dimensional maximal supergravity with metric, Kalb–Ramond field, dilaton, Ramond-Ramond zero-form, two-form and four-form potentials, and a self-dual five-form field strength. Two same-chirality Majorana-Weyl gravitini and two opposite-to-gravitino-chirality Majorana-Weyl dilatini complete its $128+128$ massless spectrum.