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. We will then modify some of the assumptions, and look for other possible CFTs. If time allows, we will study the four-point correlation functions of such models, and find out to which extent their behaviour is controlled by the fusion rules.
For an introduction to two-dimensional CFT, see my minimal lectures. The internship may last 3-6 months in the first half of 2019, and might be followed by a PhD thesis on non-rational two-dimensional CFT.
Maj : 15/11/2018 (851)