A Field-Theoretical Model of a Microemulsion

(Received 19 June 1995, received in final form and accepted 25 August 1995)

Abstract
A field-theoretical model of a microemulsion is proposed taking both, geometrical and material, degrees of freedom into account. Using methods of conformal field theory and string theory, the most relevant part of the partition function is calculated. It is shown that smooth stable surfaces exist for a physically meaningful range of control parameters. In the topological sector of spheres we prove explicitly the existence of stable surfaces with finite extension. This agrees with the well-established droplet-like phase of microemulsions. Expectation values of geometrical quantities such as the area of a surface as well as its fluctuations can be obtained. In the topological sector of tori, on the other hand, such stable configurations do not exist. This work may be considered as an application of methods of conformal field theory and string theory in another branch of physics - chemical physics and colloid science.