Instability in cosmological topologically massive gravity at the chiral point

TL;DR

At the chiral point $\mu\ell=1$, cosmological CTMG with a positive Einstein–Hilbert term exhibits a bulk mode of negative energy that grows linearly in time, signaling an instability. The authors construct this logarithmic mode as the limit of the massive and left-moving sectors, show it is not pure gauge and carries finite, time-independent energy, and reveal LCFT-like non-unitary representations of the isometry generators. They establish a well-defined variational principle with a Fefferman–Graham expansion that includes a linear-in-$\rho$ term and compute a finite, traceless, conserved boundary stress tensor, indicating the spacetime remains asymptotically AdS$_3$. Thus, chiral gravity appears to require a truncation or unitary completion to be viable, though nonperturbative stabilization remains an open question; the work also clarifies the AdS/LCFT structure and potential implications for dual theories. An erratum notes a sign correction in a key expression related to the Brown–York stress tensor.

Abstract

We consider cosmological topologically massive gravity at the chiral point with positive sign of the Einstein-Hilbert term. We demonstrate the presence of a negative energy bulk mode that grows linearly in time. Unless there are physical reasons to discard this mode, this theory is unstable. To address this issue we prove that the mode is not pure gauge and that its negative energy is time-independent and finite. The isometry generators L_0 and \bar{L}_0 have non-unitary matrix representations like in logarithmic CFT. While the new mode obeys boundary conditions that are slightly weaker than the ones by Brown and Henneaux, its fall-off behavior is compatible with spacetime being asymptotically AdS_3. We employ holographic renormalization to show that the variational principle is well-defined. The corresponding Brown-York stress tensor is finite, traceless and conserved. Finally we address possibilities to eliminate the instability and prospects for chiral gravity.