Consistent Boundary Conditions for New Massive Gravity in $AdS_3$

TL;DR

This work analyzes boundary conditions for new massive gravity in asymptotically AdS$_3$. It demonstrates that Brown-Henneaux boundary conditions are consistent for all mass values, with conserved charges vanishing at the critical point $m^2\ell^2=\tfrac{1}{2}$, hinting that the theory may be trivial there. It also studies log boundary conditions, showing they can be consistent only at the critical point and that three distinct relaxations—left-only, right-only, and both modes—lead to log-chiral gravity variants or to nonzero charges for both modes at criticality. Together, these results clarify the boundary-condition structure of NMG in AdS$_3$ and motivate further nonlinear and holographic investigations of its potential dual conformal field theories.

Abstract

In this note we study the boundary conditions for the new massive gravity theory in asymptotically $AdS_3$ spacetime. We find that the Brown-Henneaux boundary conditions are consistent with the new massive gravity for all any value of the mass parameter. At the critical point where the central charge vanishes, the conserved charges vanish, too. This provides further evidence that the theory may be trivial at the critical point under Brown-Henneaux boundary conditions. The log boundary conditions are also examined and we find that we can have three kinds of log boundary conditions for this new massive gravity theory, each of which could be consistent at the critical point, while for other value of the mass parameter, the log gravity boundary condition is not consistent.