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

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

where $\alpha$ 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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How can you find the field equations to any order? Can't you just apply the Euler-Lagrange equations to the action up to a certain order $\mathcal{O}(\alpha^n)$? –  JamalS Nov 26 at 9:34

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