Pure gravity, extremal CFTs and constraints from modularity
08.01.2009 at 16:15
It has been proposed that the dual conformal field theory to pure gravity on AdS_3 is given by an extremal 2d CFT. I will discuss the question of existence and consistency of such theories using constraints imposed by the modular properties of their partition function. After a brief review of the bosonic case, I will concentrate on pure N=2 supergravity and its dual CFT. Using modular properties of the elliptic genus, one can show that except for a few sporadic cases such extremal CFTs cannot exist. In a second part I will also discuss the relationship between modular differenial equations and null vectors and their implications for extremal CFTs.
Arnold Sommerfeld Center