Informal Pizza Seminar

Pure gravity, extremal CFTs and constraints from modularity

Christoph Keller

Harvard University

It has been proposed that the dual conformal field theory to pure gravity on AdS₃ 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 differential equations and null vectors and their implications for extremal CFTs.