Liouville field theory

In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation.

Liouville theory is defined for all complex values of the central charge ${\displaystyle c}$ of its Virasoro symmetry algebra, but it is unitary only if

${\displaystyle c\in (1,+\infty ),}$

and its classical limit is

${\displaystyle c\to +\infty .}$

Although it is an interacting theory with a continuous spectrum, Liouville theory has been solved. In particular, its three-point function on the sphere has been determined analytically.