= Trace elimination in string Faddeev-Popov gauge fixing
{title2=$\delta g_{ab}=(2\omega+\nabla\cdot v)g_{ab}+(P_1v)_{ab}$}
In two dimensions the metric variation splits into a scalar trace and the trace-free diffeomorphism operator $(P_1v)_{ab}=\nabla_av_b+\nabla_bv_a-g_{ab}\nabla\cdot v$. Integrating the Weyl parameter in the inverse <Faddeev-Popov determinant> removes the trace delta function. The remaining determinant is exponentiated by an anticommuting vector ghost and symmetric trace-free antighost, yielding the two chiral $b\bar\partial c$ terms. Conformal Killing vectors and moduli are zero modes treated separately from this local determinant.
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