There exists two distinct off-shell N = 2 supergravities in three dimensions. They are also referred to as N = (1, 1) and N = (2, 0) supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The N = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p)⊕OSp(2, q) with R-symmetry group SO(p) × SO(q). We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the N = (1, 1) invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the N = (2, 0) invariants do not allow such possibility.

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from perturbative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f (R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravityoriginally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the N = (1, 1) Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the N = 1 model but we find new solutions with a time-like Killing vector that are absent in the N = 1 case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an AdS 3 background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.

Abstract:In this paper, we show that a higher derivative theory, such as New Massive Gravity, allows the existence of new entangling surfaces with non-zero extrinsic curvature. We perform the analysis for Lifshitz and Warped AdS spacetimes, revealing the role of the higher derivative contributions in the calculation of the holographic entanglement entropy. Finally, as an outcome of our holographic analysis we briefly comment on the dual boundary theory.