= Liouville field theory
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{title2=$S_L=\frac1{4\pi}\int\sqrt h[(\nabla\phi)^2+QR\phi+4\pi\mu e^{2b\phi}]$}
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<Liouville field theory> is a two-dimensional scalar theory with a curvature background charge and an exponential interaction. In the usual spacelike normalization, quantum conformal invariance gives $Q=b+b^{-1}$ and <central charge> $c_L=1+6Q^2$. When a noncritical <string worldsheet> conformal factor is retained as a dynamical field, its effective action has this form and its <central charge> combines with the matter and <worldsheet ghost field> charges. It is closely related to a <background-charge scalar field>, but its exponential potential supplies an additional interaction.
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