Physics Group Meeting

We consider unitary Conformal Field Theory in dimensions D higher than two with a finite central charge. We assume that CFT contains conserved current of spin higher than two. We analyze the consequences of this fact. We focus on the case of D=3 and CFT with the unique stress tensor. In this case we show that the theory has an infinite number of currents and is essentially free. More precisely, we show that symmetries fix correlation functions of the conserved currents to be the free field ones up to one free parameter which is the central charge