 String-frame metric

The string-frame metric is the target metric appearing directly in the kinetic term of the string nonlinear sigma model. With conventional Euclidean dilaton $\phi$, its leading spacetime gravitational action contains $\sqrt{-g^{(s)}}{e}^{-2\phi }(R+4|\nabla \phi {|}^2)$. The dilaton-dependent Ricci coefficient distinguishes it from the Einstein-frame metric. Frame changes are local field redefinitions where the conformal factor is finite and nonzero; the Lorentzian dilaton coupling sign convention fixes which named field is $\phi$.