Critical Phenomena, Strings, and Interfaces

Traditionally, the participants of the “Ahrenshoop International Symposium on the Theory of Elementary Particles” form two nearly disjoint subsets, consisting of string theorists and lattice gauge theorists. So, for a plenary speaker the question arises: is it possible to give a talk which addresses both of these species? I don’t have an answer, but this contribution is meant as an attempt. Considering the basic theoretical objects which are being studied, there is no apparent relation. The geometrical objects of string theory are world-sheets of open or closed strings. We shall not speak about the additional internal degrees of freedom here. A parameterized world-sheet is described by functions x(σ, τ). In lattice gauge theory, on the other hand, the basic objects are group valued variables U(x, μ) associated with the links (x, μ) of a space-time lattice. That looks very different.