We introduce fuzzy field theories and give an overview of their spontaneous symmetry breaking patters. Fuzzy spaces enjoy a nontrivial short distance structure, which is reflected in some surprising ways to break the symmetry of a field theory. We then give a description of these theories in terms of hermitian matrix models. These models are a generalization of the standard random matrix models with extra terms in the probability distribution due to the kinetic term of the field theory. We present several possible ways how to deal with this modification and show to what extent they describe the desired properties of the corresponding field theory.
Jurai Tekel (Bratislava): Matrix models of fuzzy field theories
