The CFT dual of AdS gravity with torsion

Abstract

We consider the Mielke–Baekler model of three-dimensional AdS gravity with torsion, which has gravitational and translational Chern–Simons terms in addition to the usual Einstein–Hilbert action with cosmological constant. It is shown that the topological nature of the model leads to a finite Fefferman–Graham expansion. We derive the holographic stress tensor and the associated Ward identities and show that, due to the asymmetry of the left- and right-moving central charges, a Lorentz anomaly appears in the dual conformal field theory. Both the consistent and the covariant Weyl and Lorentz anomaly are determined, and the Wess–Zumino consistency conditions for the former are verified. Moreover we consider the most general solution with flat boundary geometry, which describes left- and right-moving gravitational waves on AdS3 with torsion, and show that in this case the holographic energy–momentum tensor is given by the wave profiles. The anomalous transformation laws of the wave profiles under diffeomorphisms preserving the asymptotic form of the bulk solution yield the central charges of the dual CFT and confirm the results that appeared earlier on in the literature. Finally we comment on some points concerning the microstate counting for the Riemann–Cartan black hole.