Article,
Chiral Gravity, Log Gravity and Extremal CFT
(Mar 26, 2009)
DOI: 10.1103/PhysRevD.81.064007
Abstract
We show that the linearization of all exact solutions of classical chiral
gravity around the AdS3 vacuum have positive energy. Non-chiral and
negative-energy solutions of the linearized equations are infrared divergent at
second order, and so are removed from the spectrum. In other words, chirality
is confined and the equations of motion have linearization instabilities. We
prove that the only stationary, axially symmetric solutions of chiral gravity
are BTZ black holes, which have positive energy. It is further shown that
classical log gravity-- the theory with logarithmically relaxed boundary
conditions --has finite asymptotic symmetry generators but is not chiral and
hence may be dual at the quantum level to a logarithmic CFT. Moreover we show
that log gravity contains chiral gravity within it as a decoupled charge
superselection sector. We normally evaluate the Euclidean sum over geometries
of chiral gravity and show that it gives precisely the holomorphic extremal CFT
partition function. The modular invariance and integrality of the expansion
coefficients of this partition function are consistent with the existence of an
exact quantum theory of chiral gravity. We argue that the problem of quantizing
chiral gravity is the holographic dual of the problem of constructing an
extremal CFT, while quantizing log gravity is dual to the problem of
constructing a logarithmic extremal CFT.
