# Pure gravity, extremal CFTs and constraints from modularity

Christoph Keller (Harvard)

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

Theresienstrasse 37

Room 348/349