Given a bosonic string theory defined by the action
$$\tag1 S = \frac{1}{4\pi \alpha'}\int_\Sigma \! \mathrm{d}^2 \sigma \, \sqrt{|g|} \, \left[ G_{\mu\nu} \partial_\alpha X^\mu \partial_\beta X^\nu g^{\alpha \beta} +i B_{\mu \nu}\partial_\alpha X^\mu \partial_\beta X^\nu \epsilon^{\alpha \beta} + \alpha' \Phi R^{(2)}\right],$$ a sufficient condition for the quantum Weyl invariance of this theory is given, up to acertar order, by the set of equations for the beta functions:
$$0 =\beta_{\mu\nu}(G) = \alpha'R_{\mu\nu} + 2\alpha'\nabla_\mu\nabla_\nu \Phi - \frac{\alpha'}{4}H_{\mu\lambda \kappa}H^{\lambda \kappa}_\nu \tag2$$
$$0=\beta_{\mu\nu}(B) = -\frac{\alpha'}{2}\nabla^\lambda H_{\lambda\mu\nu} + \alpha' \nabla^\lambda \Phi H_{\lambda \mu \nu} \tag3$$
$$0=\beta(\Phi) = -\frac{\alpha'}{2}\nabla^2 \Phi + \alpha' \nabla_\mu \Phi \nabla^\mu \Phi -\frac{\alpha'}{24}H_{\mu\nu\lambda}H^{\mu\nu\lambda}\tag4,$$ See, for instance, section $3.7$ of Polchinski String Theory vol.1. These equations are stated in other String Theory textbooks such as the one by Blumenhagen.
Some of these terms are obtained in several papers such as in reference $[1]$ by means of dimensional regularization, which involves writing the fields $G, B, \Phi$ in $(1)$ as bare couplings in terms of renormalized couplings and counter terms that appear when calculating the partition function perturbatively.
My question is: are the fields that appear in the beta functions $(2),(3),(4)$ associated with the renormalized couplings or the bare couplings?
References:
$[1]$ A.A. Tseytlin SIGMA MODEL APPROACH TO STRING THEORY $(1989)$
