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.

References

Paradigms	Classical theories of gravitation Quantum gravity Theory of everything

Classical	Einstein–Cartan Bimetric theories Gauge theory gravity Teleparallelism Composite gravity f(R) gravity Massive gravity Modified Newtonian dynamics (MOND) Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström Whitehead Geometrodynamics Induced gravity Tensor–vector–scalar Chameleon Pressuron

Quantisation	Euclidean quantum gravity Canonical quantum gravity Wheeler–DeWitt equation Loop quantum gravity Spin foam Causal dynamical triangulation Causal sets DGP model

Unification	Kaluza–Klein theory Dilaton Supergravity

Unification and quantisation	Noncommutative geometry Self-creation cosmology Semiclassical gravity Superfluid vacuum theory Logarithmic BEC vacuum String theory M-theory F-theory Heterotic string theory Type I string theory Type 0 string theory Bosonic string theory Type II string theory Little string theory Twistor theory Twistor string theory

Generalisations / Extensions of GR	Liouville gravity Lovelock theory (2+1)-dimensional topological gravity Gauss–Bonnet gravity Jackiw–Teitelboim gravity

Central concepts

Approaches

String theory	Bosonic string theory M-theory Supergravity Superstring theory

Canonical quantum gravity	Loop quantum gravity Wheeler–DeWitt equation

Euclidean quantum gravity	Hartle–Hawking state

Others	Causal dynamical triangulation Causal sets Noncommutative geometry Spin foam Group field theory Superfluid vacuum theory Twistor theory

Toy models

Applications

Quantum cosmology	Eternal inflation Multiverse FRW/CFT duality