Logarithmic conformal field theory approach to topologically massive gravity

TL;DR

This paper investigates topologically massive gravity at the chiral point using logarithmic conformal field theory, revealing no physical propagating degrees of freedom due to unphysical field pairs.

Contribution

It introduces new tensor fields to identify physical modes but demonstrates they form unphysical pairs, clarifying the nature of degrees of freedom at the chiral point.

Findings

No physically propagating degrees of freedom at the chiral point.

New tensor fields are unphysical and form ghost pairs.

X is not a primary field, indicating no physical modes.

Abstract

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.