Liouville gravity

Liouville gravity 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 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.

See also

• Liouville field theory
• CGHS model
• Jackiw–Teitelboim gravity