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Usually one finds this expression for the low energy action

$$S = \frac{1}{2\kappa_0^2}\int d^D X\; \sqrt{-G}\; \mathrm{e}^{-2\Phi}\,(R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4 \partial_{\mu}\Phi\partial^{\mu}\Phi).$$

On dimensional grounds one can deduce $\kappa_0^2$ near $\ell_s^{24}$ (for $D=26$) or $\ell_s^8$ (for $D=10$).

Some authors use (obvious for the superstring, not for $D=26$ string):

$$2\kappa_0^2=(2\pi)^7\alpha'^4$$ with $\ell_s=2\pi\sqrt{\alpha'}$. Btw. this also confuses me, is $\ell_s=\sqrt{\alpha'}$?

So my question is how is $2\kappa_0^2$ determined?

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