Logarithmic AdS waves and Zwei-Dreibein gravity

Abstract

We show that the parameter space of Zwei-Dreibein Gravity (ZDG) in AdS 3 exhibits critical points, where massive graviton modes coincide with pure gauge modes and new 'logarithmic' modes appear, similar to what happens in New Massive Gravity. The existence of critical points is shown both at the linearized level, as well as by finding AdS wave solutions of the full non-linear theory, that behave as logarithmic modes towards the AdS boundary. In order to find these solutions explicitly, we give a reformulation of ZDG in terms of a single Dreibein, that involves an infinite number of derivatives. At the critical points, ZDG can be conjectured to be dual to a logarithmic conformal field theory with zero central charges, characterized by new anomalies whose conjectured values are calculated.

Anisotropic scale invariant spacetimes and black holes in Zwei-Dreibein Gravity

“…The same happens for the AdS waves studied in [18]. In the latter case, the metric associated to e 1 is given by…”

“…The fact that bigravity theories can be viewed as higher-derivative theories of one metric field was first noticed in [30]. A similar procedure was followed in [18] for the ZDG case. To see this, first we observe that we can solve the equations of motion (3.2a) to obtain an expression for e 2 a in terms of e 1 a .…”

“…It was shown in [18] that this bigravity theory can be viewed as a higher-derivative gravity theory of which NMG is a particular limit. Some indications were found in [18] that ZDG at some particular points of the parameter space can be interpreted as a gravity dual of the Logarithmic Conformal Field Theories (LCFT) [19], which are also relevant in the context of condensed matter. Hence, a natural question is whether ZDG can also be used in non-relativistic extensions of the AdS/CFT correspondence.…”

“…5 In the footnote 4 of ref. [18] the authors said that it is possible to find the inverse of e2 as a power expansion in 1/m 2 . On the other hand, even when the invertibility on the dreibein e2 is not imposed as a necessary condition, notice that the explicit solutions we found here for the two spin-two fields are manifestly invertible.…”

“…These are a special case of the AdS-waves studied in [18], for which the wave profile functions (3.4) takes the values f + (u) = 0, f − (u) = f 0 , and n − = −2ν. The dreibein e 1 in this case is given by e 11 = ℓ y ℓ ν y ν du + y ν ℓ ν dv , e 12 = ℓ y y ν ℓ ν dv , e 13 = ℓ y dy , while e 2 is given by…”