# Expectation of 2-form field $B_{MN}$ in string theory

In the context of string theory, in particular when we're dealing with a low energy effective action, if we have an effective action of the form:

$$S_{eff} \sim S^{(0)} + \alpha S^{(1)} + (\alpha)^2 S^{(2)} + \ldots$$

In which $\alpha$ is the Regge slope:

$$S^{(0)} \sim \int\limits d^Dx H_{MNP}H^{MNP}$$

and $H_{MNP} = \partial_M B_{NP} + \partial_N B_{PM} +\partial_P B_{MN}$.

When we are asked to put $H_{MNP}=0$ to compute the list of terms corresponding to the tensor expectation relative to the field, what are we supposed to do exactly?

One more question: How can we find the field equations of the tensor to any order?

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