Three-dimensional tricritical gravity

Abstract

We consider a class of parity-even, six-derivative gravity theories in three dimensions. After linearizing around anti-de Sitter space, the theories have one massless and two massive graviton solutions for generic values of the parameters. At a special, so-called tricritical, point in parameter space the two massive graviton solutions become massless, and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. The theory at this point is conjectured to be dual to a rank-3 logarithmic conformal field theory whose boundary stress tensor, central charges, and new anomaly we calculate. We also calculate the conserved Abbott-Deser-Tekin charges. At the tricritical point, these vanish for excitations that obey Brown-Henneaux and logarithmic boundary conditions, while they are generically nonzero for excitations that show logarithmic-squared boundary behavior. This suggests that a truncation of the tricritical gravity theory and its corresponding dual logarithmic conformal field theory can be realized either via boundary conditions on the allowed gravitational excitations, or via restriction to a zero-charge subsector. We comment on the structure of the truncated theory.

Critical gravity in the Chern–Simons modified gravity

“…However, it seems difficult to derive a massive graviton with 5 DOF propagating in the AdS 4 spacetimes from the Chern-Simons modified gravity, compared to the higher curvature gravity [9]. This is mainly because massive excitations depend critically on the choice of coupling field v c (θ).…”

“…Instead of massive gravitons, an equal amount of logarithmic modes appears in the theory [9]: 1 DOF for topologically massive gravity (TMG) [10], 2 DOF for new massive gravity [11,12,13], 5 DOF for higher curvature gravity in 4D [5]. In general, we have D(D + 1)/2 − (D + 1) DOF for massive graviton.…”

Tricritical gravity waves in the four-dimensional generalized massive gravity

“…A difference between the 4DGMG and 3DGMG is that the former has the Chern-Simons term of θ 4 * RR with θ a nondynamical field, while the latter has the topologically massive in [16,21,26]. On the other hand, the compact equation (3.6) expressed in one-dimensional operators is obtained only after choosing the AdS-wave.…”

“…Two tricritical points emerged in the 3DGMG parameter space, whose dual theory is a rank-3 LCFT [24]. A truncation of the tricritical 3DGMG could be made by imposing Q L = 0 with Q L the Abbott-Deser-Tekin charge for log-square boundary conditions [16]. After truncation, a left-moving sector of CFT remains as a unitary theory.…”

“…A 3D six-derivative tricritical gravity was treated as a dual to a rank-3 LCFT [16], while a four-derivative critical gravity in four dimensions was considered as a dual to a rank-3…”