On the Generalized Minimal Massive Gravity

TL;DR

This paper investigates the properties of the Generalized Minimal Massive Gravity (GMMG) in asymptotically AdS_3 space, demonstrating its consistency, holographic duality with LCFT, and absence of ghosts, with potential reductions to other models.

Contribution

It introduces GMMG with additional deformation terms, analyzes its linearized excitations, and establishes its unitarity, holographic dual, and ghost-free nature, extending previous massive gravity models.

Findings

GMMG has massless graviton solutions at the tricritical point.

The theory is free of negative-energy bulk modes.

GMMG avoids bulk-boundary unitarity clash and has no Boulware-Deser ghosts.

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.