# Beta function of the non-linear sigma model

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In chapter 7.1.1. in Tong's notes about String Theory could someone sketch how can I show the statements that he nmakes around eq. 7.5

• That the addition of the counterterm can be absorbed by renormalization the wavefunction and the metric

• How does he conclude from the renormalization $$G_{\mu \nu} \rightarrow G_{\mu \nu} + \dfrac{\alpha '}{\epsilon}\mathcal{R}_{\mu\nu}$$ that the beta function equals $$\beta_{\mu\nu}(G) = \alpha ' \mathcal{R}_{\mu \nu} \quad ?$$

This post imported from StackExchange Physics at 2014-10-01 22:39 (UTC), posted by SE-user Anne O'Nyme