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[tex]

S=-\frac{1}{2\lambda_{\text{s}}^{d-1}}\int d^{d+1}x\sqrt{|g|}e^{-\phi}\left[R+(\nabla\phi)^2+2\lambda_{\text{s}}^{d-1}V(\phi)-\frac{1}{12}H^2\right]+S_m

[/tex]

where

[tex]

H^2=H_{\mu\nu\alpha}H^{\mu\nu\alpha}\\

H_{\mu\nu\alpha}=\partial_\mu B_{\nu\alpha}+\partial_\nu B_{\alpha\mu}+\partial_{\alpha} H_{\mu\nu}

[/tex]

and [itex]B_{\mu\nu}[/itex], [itex]\phi[/itex] and [itex]R[/itex] are antisymmetric tensor, dilaton, Ricci scalar on target space respectively.

Effective action can be derived by expanding the [itex]\sigma[/itex]-model action in powers of [itex]R[/itex].

But where do the matter sector [itex]S_m[/itex] and ambiguity of dilation potential [itex]V(\phi)[/itex] come from?

If this action can be derived by this way, I'm afraid the effective action is determined uniquely and new matter fields don't appear.

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# Low curvature effective action in string theory

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