# 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

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

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.