Holographic RG Flows from Quasi-Topological Gravity

Abstract

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].

Holographic (a,c) charges and their universal relation in d=6 from massless higher-order gravities

“…(The precise ratio C T /C T is given in (3.12).) (This result was also derived in the general off critical case in quasi-topological gravity [11].) To clarify the equation further, we note that higher-order gravities involve the bare cosmological constant Λ 0 and α i 's that denote the couplings of higher-order terms.…”