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