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# Liouville gravity

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 Title: Liouville gravity Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Liouville gravity

Liouville gravity[1][2] is a model of gravity in one spatial and one time dimension with a dilaton. It has the specific coupling of the form

S = \frac{1}{4\pi}\int d^2x\sqrt{-g} \left[ \left( b+ b^{-1} \right)\Phi R + \left( \nabla\Phi \right)^2 + 4\pi \mu e^{2b\Phi} \right],

where Φ is the dilaton field. It should not be confused[3][4] with the CGHS model or Jackiw–Teitelboim gravity. After taking quantum conformal anomalies into account, it turns out to be a conformal field theory. This model is used in the study of non-critical string theory.