Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes

Abstract

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS 2 × S 3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS 2 × S 3 geometries can in turn be connected to AdS 5 spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS 5 spacetime. The asymptotic AdS 5 spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points.

Charged dilatonic black holes in gravity’s rainbow

“…In the IR limit this gravity reduces to general relativity, and so it can be considered as a UV completion of general relativity. Motivated by this work on Horava-Lifshitz gravity, different Lifshitz scalings for space and time have been considered for type IIA string theory [3], type IIB string theory [4], the AdS/CFT correspondence [5][6][7][8], dilatonic black branes [9,10], and dilatonic black holes a e-mail: hendi@shirazu.ac.ir b e-mail: f2mir@uwaterloo.ca c e-mail: behzad.eslampanah@gmail.com d e-mail: sh.panahiyan@gmail.com [11,12]. Another UV completion theory of general relativity which reduces to general relativity in the IR limit is called gravity's rainbow [13].…”

Constraints on renormalization group flows from holographic entanglement entropy

“…We want to examine the relations (17) which guarantee dc d /dr m ≥ 0, and ask when they can be realized. In general, the conditions (7) and (8) do not constrain the signs of f and g. However, if additionally f UV ≤ 0 and g UV ≤ 0 (21) then the NEC imply that both f and g are non-positive along the entire RG flow. Thus, whenever (21) holds, f g ≥ 0 everywhere and the candidate c-function behaves as it should, decreasing monotonically towards lower energies (A ′ (r m ) ≥ 0 immediately follows from f ∝ −A ′ ).…”

Holographic RG flows with nematic IR phases

“…Domain-wall solutions interpolating between different Lifshitz geometries, or between Lifshitz and AdS, have been constructed in a number of setups, typically involving gravity coupled to a massive U(1) gauge field -and sometimes a scalar -and their generalizations (see e.g. [34,[36][37][38]). As a concrete example, flows of this type can be obtained (see e.g.…”