= One-loop metric beta function of a string sigma model
{title2=$\beta^g_{ab}=\alpha'R_{ab}+O(\alpha'^2)$}
For the Euclidean kinetic normalization $(4\pi\alpha')^{-1}\int g_{ab}(X)\partial X^a\partial X^b$, vanishing two-form and constant <dilaton>, the leading beta function is $\beta^g_{ab}=\alpha'R_{ab}$. The covariant Gaussian fluctuation operator contains a curvature vertex whose one-loop trace contracts to the <Ricci tensor>. Its logarithmic divergence renormalizes the metric. The scale convention is $\beta=\mu\,dg/d\mu$; Weyl consistency requires vanishing of this beta function as well as the other anomaly coefficients.
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