On the Generalized Minimal Massive Gravity

Abstract

In this paper we study the Generalized Minimal Massive Gravity (GMMG) in asymptotically $AdS_3$ background. The generalized minimal massive gravity theory is realized by adding the CS deformation term, the higher derivative deformation term, and an extra term to pure Einstein gravity with a negative cosmological constant. We study the linearized excitations around the $AdS_3$ background and find that at special point (tricritical) in parameter space the two massive graviton solutions become massless and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. So it is natural to proposed that GMMG model could also provide a holographic description for a $3-$rank Logarithmic Conformal Field Theory (LCFT). We calculate the energy of the linearized gravitons in $AdS_3$ background, and show that the theory is free of negative-energy bulk modes. Then we obtain the central charges of the CFT dual explicitly and show GMMG also avoids the aforementioned "bulk-boundary unitarity clash". After that we show that General Zwei-Dreibein Gravity (GZDG) model can reduce to GMMG model. Finally by a Hamiltonian analysis we show that the GMMG model has no Boulware-Deser ghosts and this model propagate only two physical modes.