The 2D effective field theory of interfaces derived from 3D field theory

The one--loop determinant computed around the kink solution in the 3D $\phi^4$ theory, in cylindrical geometry, allows one to obtain the partition function of the interface separating coexisting phases. The quantum fluctuations of the interface around its equilibrium position are described by a $c=1$ two--dimensional conformal field theory, namely a 2D free massless scalar field living on the interface. In this way the capillary wave model conjecture for the interface free energy in its gaussian approximation is proved.