Minimal massive supergravity and new theories of massive gravity

We present an action for minimal massive gravity (MMG) in three dimensions in terms of a dreibein and an independent spin connection. Furthermore, the construction provides an action principle for an infinite family of so-called third-way consistent generalizations of the three-dimensional Einstein field equations, including exotic massive gravity and new higher-order generalizations. It allows us to systematically construct the matter couplings for these models, including the couplings to fermions, depending on the spin connection. In particular, we construct different supersymmetric extensions of MMG, and derive their second order fermionic field equations. This establishes a new class of three-dimensional supergravity theories and we discuss their limit to topological massive supergravity. Finally, we identify the landscape of (anti–)de Sitter vacua of the supersymmetric models. We analyze the spectrum and the unitarity properties of these vacua. We recover the known AdS vacua of MMG which are bulk and boundary unitary.

Figure 1

Different regions in the parameter space of bosonic models. As long as the MMG model possesses an AdS vacuum, i.e. with the exception of the gray and yellow areas, it admits at least one supersymmetric extension. Along the parabola (4.25), there is always one Minkowski vacuum together with an (a)dS vacuum. The red line is the so-called merger line [19], $\mathrm{\Gamma }=0$, in which both (a)dS vacua of the model coincide. The dashed blue line is the chiral line (4.33) on which one of the central charges of the dual theory vanishes. The AdS vacua avoiding the bulk/boundary unitarity clash are all situated in region V, c.f. Sec. 4e.

Figure 2

Different regions in the parameter space of supersymmetric models as a function of the parameter $\eta$. The blue lines correspond to the parabola (4.25) of Fig. 1, separating the different regions. The red line is the merger line, in which both (a)dS vacua of the model coincide. The dashed lines are the chiral lines (4.35), (4.36) on which one of the central charges of the dual theory vanishes. This map is a covering of part of Fig. 1 with different supersymmetric models mapping onto the same bosonic model as indicated for the different regions. The AdS vacua avoiding the bulk/boundary unitarity clash are all situated in region V, they are supersymmetric for $\eta <0$ and nonsupersymmetric for $\eta >0$, cf. Sec. 4e.