Logarithmic conformal field theory approach to topologically massive gravity

We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of $\psi^{new}$ and $X$ are introduced for a candidate of propagating physical field at the chiral point. However, we show that ($\psi^{new},\psi^L$) form a dipole ghost pair of unphysical fields and $X$ is not a primary. This implies that there is no physically propagating degrees of freedom at the chiral point.