# Low curvature effective action in string theory

1. Aug 26, 2014

### synoe

String effective action:
$$S=-\frac{1}{2\lambda_{\text{s}}^{d-1}}\int d^{d+1}x\sqrt{|g|}e^{-\phi}\left[R+(\nabla\phi)^2+2\lambda_{\text{s}}^{d-1}V(\phi)-\frac{1}{12}H^2\right]+S_m$$
where
$$H^2=H_{\mu\nu\alpha}H^{\mu\nu\alpha}\\ H_{\mu\nu\alpha}=\partial_\mu B_{\nu\alpha}+\partial_\nu B_{\alpha\mu}+\partial_{\alpha} H_{\mu\nu}$$
and $B_{\mu\nu}$, $\phi$ and $R$ are antisymmetric tensor, dilaton, Ricci scalar on target space respectively.

Effective action can be derived by expanding the $\sigma$-model action in powers of $R$.
But where do the matter sector $S_m$ and ambiguity of dilation potential $V(\phi)$ 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.

2. Sep 1, 2014