= Bosonic sigma-model Weyl anomaly coefficients
{title2=$\overline\beta^G=\overline\beta^B=\overline\beta^\Phi=0$}
To first order in $\alpha'$, the conventional Euclidean <dilaton> coupling gives $\overline\beta^G_{\mu\nu}=\alpha'[R_{\mu\nu}-H_{\mu\rho\sigma}H_\nu{}^{\rho\sigma}/4+2\nabla_\mu\nabla_\nu\Phi]$ and $\overline\beta^B_{\mu\nu}=\alpha'[-\nabla^\rho H_{\rho\mu\nu}/2+(\nabla^\rho\Phi)H_{\rho\mu\nu}]$. The scalar coefficient is $(d-26)/6+\alpha'[(\nabla\Phi)^2-\nabla^2\Phi/2-H^2/24]$. Here $H$ is the <Kalb-Ramond field strength>. Vanishing of these coefficients, including higher-order corrections, is the background-field condition for quantum <Weyl transformations> to remain a gauge symmetry. The scalar coefficient includes the <central charge> deficit and is not implied by the metric equation alone.
Back to article page
