Abstract / Résumé :
The aim of this internship is to solve some simple two-dimensional conformal field theories using the conformal bootstrap method. In contrast to higher-dimensional CFTs where the conformal bootstrap ideas are implemented numerically, certain two-dimensional CFTs can be explored analytically. This is the case of minimal models, a class of particularly simple CFTs that includes the critical Ising model.
In this internship we will use an elementary approach based on fusion rules for rederiving minimal models, and the corresponding values of the Virasoro central charge. We will then investigate which generalizations of minimal models exist at other values of the central charge. And we will study the four-point correlation functions of such models, in order to find out to which extent their behaviour is controlled by the fusion rules, and to which extent by subtler properties of conformal blocks.
For an introduction to two-dimensional CFT, see my “minimal lectures”. The internship might be followed by a PhD thesis on non-rational two-dimensional CFT.