THE 2D EFFECTIVE-FIELD THEORY OF INTERFACES DERIVED FROM 3D FIELD-THEORY

The one-loop determinant computed around the kink solution in the 3D p hi(4) theory, in cylindrical geometry, allows one to obtain the partit ion function of the interface separating coexisting phases. The quantu m fluctuations of the interface around its equilibrium position are de scribed by a c = 1 two-dimensional conformal field theory, namely a 2D free massless scalar field living on the interface. In this way the c apillary wave model conjecture for the interface free energy in its ga ussian approximation is proved.