Topologically massive gravity at the chiral point is not unitary

A recent paper [1] claims that topologically massive gravity contains only chiral boundary excitations at a particular value of the Chern-Simons coupling. On the other hand, propagating bulk degrees of freedom with negative norm were found even at the chiral point in [2]. The two references use very different methods, making comparison of their respective claims difficult. In this letter, we use the method of [1] to construct a tower of physical propagating bulk states satisfying standard AdS boundary conditions. Our states have finite norm, with sign opposite to that of right-moving boundary excitations. Our results thus agree with [2] and disagree with [1].