In Volume 1 of Polchinski's String Theory book, the author works with energy--momentum tensor of CFTs till chapter 3 in a normal ordered mode, i.e. $T(z)= : \text{something}: (z)$. However, in chapter3, specifically in section $3.7$ where he treats string in curved space-time, Polchinski seems to abandon the normal ordering thing, because in equation $(3.7.12)$ he works with
$$-2\alpha' T^a_a = \beta^G_{\mu \nu} g^{ab} \partial_a X^\mu \partial_b X^\nu + i\beta^B_{\mu \nu} \epsilon^{ab} \partial_a X^\mu \partial_b X^\nu + \alpha' \beta^\Phi R,\tag1$$
But shouldn't be this be
$$-2\alpha' T^a_a = \beta^G_{\mu \nu} g^{ab} :\partial_a X^\mu \partial_b X^\nu: + i\beta^B_{\mu \nu} \epsilon^{ab} :\partial_a X^\mu \partial_b X^\nu: + \alpha' \beta^\Phi R\tag2$$ where Ricci scale terms are all also normal ordered? Why he simply drop out the normal ordering symbols?
