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

TL;DR

This paper derives a 2D effective field theory for interfaces from 3D field theory, confirming the capillary wave model conjecture by analyzing quantum fluctuations via a conformal field theory approach.

Contribution

It provides a rigorous derivation of the 2D interface theory from 3D field theory, establishing the connection with conformal field theory and validating the capillary wave model.

Findings

Quantum fluctuations described by a c=1 conformal field theory.

Proof of the capillary wave model conjecture in the Gaussian approximation.

Partition function of the interface obtained from 3D $^4$ theory.

Abstract

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.