- #1
synoe
- 23
- 0
String effective action:
<br /> 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<br />
where
<br /> H^2=H_{\mu\nu\alpha}H^{\mu\nu\alpha}\\<br /> H_{\mu\nu\alpha}=\partial_\mu B_{\nu\alpha}+\partial_\nu B_{\alpha\mu}+\partial_{\alpha} H_{\mu\nu}<br />
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.
<br /> 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<br />
where
<br /> H^2=H_{\mu\nu\alpha}H^{\mu\nu\alpha}\\<br /> H_{\mu\nu\alpha}=\partial_\mu B_{\nu\alpha}+\partial_\nu B_{\alpha\mu}+\partial_{\alpha} H_{\mu\nu}<br />
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.