On the generalized minimal massive gravity

Abstract

In this paper we study the Generalized Minimal Massive Gravity (GMMG) in asymptotically AdS3 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 AdS3 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 propose 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 AdS3 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 propagates only two physical modes.