Low energy effective action of bosonic string different in GSW and Polchinski/Tong?

Question

In Superstring Theory vol.1 by Green, Schwarz and Witten (GSW) the low energy effective action of the bosonic string is given by:

$$S=-\frac{1}{2k_0^2}\int d^{26}x\sqrt{-g}e^{-2\Phi}({\cal R}-4\partial_\mu\Phi\partial^\mu\Phi+\frac{1}{12}H_{\mu\nu\rho}H^{\mu\nu\rho}).\tag{GSW3.4.57}$$

But in String Theory vol.1 by Polchinski and in David Tong's online lectures on string theory the low energy effective action of the bosonic string is given by:

$$S=\frac{1}{2k_0^2}\int d^{26}x\sqrt{-g}e^{-2\Phi}({\cal R}+4\partial_\mu\Phi\partial^\mu\Phi-\frac{1}{12}H_{\mu\nu\rho}H^{\mu\nu\rho}). \tag{P3.7.20/T7.16}$$

As far as I can tell they are using the same conventions so why the difference?

Answer 1

Since all the mentioned authors use the same Minkowskian signature $(-,+,\ldots, +)$, it seems the difference is caused by different sign convention for the scalar curvature.