Jurai Tekel (Bratislava): String modes and fuzzy field theories in string modes formalism

Fuzzy spaces are, among other things, toy models for spaces with a discrete structure at small distances. As such, they provide a laboratory to study the consequences of this discreteness on the properties of physical theories, for example, the theory of scalar fields. The standard approach to this theory is very similar to the usual treatment of field theories on continuous spaces - momentum basis, Feynman diagrams, and loop integrals. In this talk, we present a different formulation of the scalar field theory on the fuzzy sphere - in terms of the string modes, which are functions optimally localized in position and momentum space. We will first introduce the string modes and highlight their most important properties. Then, we will show how they greatly simplify the computation of loop contributions in scalar field theory in position space and lead to some new insights into the structure of the effective action.