New massive gravity domain walls

Abstract

The properties of the asymptotic AdS 3 space-times representing flat domain walls (DW's) solutions of the New Massive 3D Gravity with scalar matter are studied. Our analysis is based on I st order BPS-like equations involving an appropriate superpotential. The Brown-York boundary stress-tensor is used for the calculation of DW's tensions as well as of the CF T 2 central charges. The holographic renormalization group flows and the phase transitions in specific deformed CF T 2 dual to 3D massive gravity model with quadratic superpotential are discussed.1 Although the NMG action (1) involves up to fourth order derivatives of 3D metrics g µν , the corresponding equations for the DW's (2) are of second order:σ +σφ − V ′ (σ) = 0 3 although there exist controversy claims concerning its super-renormalizability [4].

Self-duality from new massive gravity holography

“…The main ingredients of the NMG holography -the NMG's vacua and DW's solutions, the values of the central charges of the conjectured dual CF T 2 's and the holographic RG flows -were extensively studied by different methods [17,20,21,27,29,30]. As is well known from the example of Einstein gravity [35] ,the properties and the proper existence of the holographic RG flows in its 2d dual QFT 2 , strongly depend on the form of bulk matter interactions.…”

“…More precisely, we shall address the question of how can one derive the "holographic gravitational" counterparts of certain duality symmetries, such as the above mentioned inversions and fractional linear transformations. We consider the 3-dimensional New Massive Gravity (NMG) model [17], coupled to scalar self-interacting matter, and will look for the specific restrictions to be imposed on the form of the matter superpotential in order to ensure the strong-weak coupling self-duality of the corresponding two-dimensional pCFT 2 , constructed by the methods of the NMG holography [28][29][30]32].…”

“…The recent progress in the understanding of the t'Hooft limits (N, k → ∞ but finite N N +k ) of certain cosets of SU(N ) k WZW models (as for example the W N minimal models) as an appropriate higher spin extension of the 3d Einstein gravity [14][15][16] has renewed the interest in the identification of appropriate limits of the most famous family of CFT 2 's -the BPZ and the Liouville minimal models [11] -as holographic duals of certain extended 3d gravity models [28][29][30]32]. There exists an indication that the holographic description of these CFT 2 's in the case of relatively large, but finite central charges, can be achieved by considering the quantum 3d gravity contributions beyond the (semi-)classical one [16], or/and of certain "higher curvature" extensions of the Einstein gravity, including powers of the curvature and of the Ricci tensor at the classical level.…”

“…It is then natural to expect that appropriate perturbations of these CFT's give rise to certain strong-weak coupling self-dual non-conformal pCF T 2 's we are interested in. Although the proper identification of the CFT 2 's dual to NMG model (1.1), is not yet fully understood, the off-critical AdS/CFT methods based on the DW's solutions of NMG model coupled to massive self-interacting scalar field with an action [29,31]:…”

“…as well as the NMG holographic RG results related to them [29,30], provide the necessary tools for the selection of the conditions on the NMG-matter interactions which lead to such self-dual pCFT 2 's.…”