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