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].

The properties of an extension of the New Massive 3D Gravity by scalar matter with Higgs-like self-interaction are investigated. Its peturbative unitarity consistency is verified for a family of cosmological Bounce solutions found by the superpotential method. They correspond to the lower bound λ = −1 of the BHT unitarity window and describe eternally accelerated 3D Universe between two initial/final stable dS 3 vacua states. 1

We investigate the holographic Renormalization Group (RG) flows and the critical phenomena that take place in the QF T 's dual to the d-dimensional cubic Quasi-Topological Gravity coupled to scalar matter. The knowledge of the corresponding flat Domain Walls (DWs) solutions, allows us to derive the explicit form of the QF T 's beta -functions, as well as of the trace anomalies a(l) and c(l), in terms of the matter superpotential. As a consequence we are able to determine the complete set of CF T data characterizing the universality classes of the UV and IR critical points and to follow the particular RG evolution of this data. We further analyse the dependence of the critical properties of such dual QF T 's on the values of the Lovelock couplings and on the shape of the superpotential. For odd values of d, the explicit form of the "a and c -central charges" as functions of the running coupling constant, enable us to establish the conditions under which the a/c -Theorems for their decreasing are valid. The restrictions imposed on the massless Holographic RG flows by the requirements of the positivity of the energy fluxes are derived. The particular case of quartic Higgs-like superpotential is studied in detail. It provides an example of unitary dual QF T 's having few c = a critical points representing second or infinite order phase transitions. Depending on the range of the values of the coupling constant they exhibit massive and massless phases, described by a chain of distinct DWs solutions sharing common boundaries. A The proof of d ≥ 7 a/c-Theorems 63 A.1 µ + model 63 A.2 µ − model 65 B GB domain walls for negative λ 66 U V /IR 4's.2 see for example ref.[9] for recent discussion. 3 determined by the central charges a U V /IR and c U V /IR , or asymptotically by the number of colors (N 2 c )UV ≈ (LUV /l pl ) 3 of the corresponding SU (Nc) CF T U V /IR 4 . 6 we have denoted W ′ (σ) = dW dσ and σ = dσ dy 7 one can always find an appropriated range of values of the gravitational couplings λ and µ (not both negative), such that at least one of the vacua of the Lovelock gravity-matter model (2.1) to be of topological nature, as it is demonstrated in Sect.3 of ref. [5].

We investigate the holographic renormalization group flows and the classical phase transitions that occur in two-dimensional QFT model dual to the New Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions generated by quadratic superpotential are considered. The off-critical AdS 3 /CFT 2 correspondence determines the exact form of the QFT 2 's β-function and the singular part of the reduced free energy. The corresponding scaling laws and critical exponents characterizing the RG fixed points as well as the values of the mass gaps in the massive phases are obtained. Int. J. Mod. Phys. A 2013.28. Downloaded from www.worldscientific.com by THE UNIVERSITY OF OKLAHOMA on 02/02/15. For personal use only. 1350073-17 Int. J. Mod. Phys. A 2013.28. Downloaded from www.worldscientific.com by THE UNIVERSITY OF OKLAHOMA on 02/02/15. For personal use only.

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