Topologically Massive Gravity at the Chiral Point is Not Unitary

TL;DR

This paper demonstrates that topologically massive gravity at the chiral point admits propagating bulk states with finite norm, challenging previous claims of its unitarity and chiral boundary excitations.

Contribution

It constructs bulk propagating states at the chiral point using a different method, showing they have finite norm and contradicting earlier claims of chirality and unitarity.

Findings

Bulk states with finite norm exist at the chiral point.

These states have opposite sign to boundary excitations.

Results challenge previous claims of chirality and unitarity.

Abstract

A recent paper [arXiv:0801.4566] 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 were found even at the chiral point in [arXiv:0803.3998]. The two references use very different methods, making comparison of their respective claims difficult. In this letter, we use the method of [arXiv:0801.4566] to construct a tower of 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 [arXiv:0803.3998] and disagree with [arXiv:0801.4566].