Abstract
We provide a ``user-friendly'' algorithm to systematically and rapidly obtain exact planar black hole solutions in the Einstein-Maxwell theory deformed by the most general shift- and reflection-symmetric Horndeski sector where the usual Galileon is replaced by a tuple of scalars with profiles linear in the coordinates of the transverse manifold. Under precise assumptions, these axion backgrounds break the translational invariance of the system, causing momentum dissipation in the holographically dual field theory. The success of the method relies on the simple realization that the bulk equations of motion become more tractable when written in terms of the axions kinetic terms, instead of the radial coordinate. Showcasing this particularly efficient recipe, we derive novel asymptotically AdS black holes, and show that their extremal counterparts always flow to an $\mathrm{AdS}_2\times \mathbb{R}^2$ infrared fixed point. Additionally, we report an interesting family of new asymptotically Lifshitz black hole solutions with $z>1$. Finally, we discuss the DC transport properties of the dual relativistic field theories in view of possible applications to condensed matter systems.
Highlights
With the advent of the anti-de Sitter/conformal field theory (AdS=CFT) correspondence [1] and the subsequent advances in “bottom-up” holography [2,3], hairy black holes have become interesting theoretical laboratories offering a fresh insight into the physics of strongly correlated systems, in the context of an AdS/condensed matter theory duality [4]
Relevant when dealing with such gauge/ gravity models, planar black holes, that is, black holes with a Riemann-flat transverse manifold, have their own place in the “black” landscape of gravitational theories
Based on the logic behind this prescription, and armed only with a minimal set of initial assumptions, we will be able to pull off a complete derivation of the dc transport matrix for relativistic field theory duals, without the need to fix the Gn’s a priori
Summary
With the advent of the anti-de Sitter/conformal field theory (AdS=CFT) correspondence [1] and the subsequent advances in “bottom-up” holography [2,3], hairy black holes have become interesting theoretical laboratories offering a fresh insight into the physics of strongly correlated systems, in the context of an AdS/condensed matter theory duality [4]. To keep the total energy of the boundary field theory conserved, and the time component of the boundary Ward identity unmodified, i.e., ∂aTat 1⁄4 0, we do not break time diffeomorphisms in the bulk This can be ensured by considering a minimal set of scalar fields given by φI 1⁄4 pδIjxj; ð1Þ where the index j 1⁄4 1; ...; d only spans the coordinates of the transverse manifold and δIi is an isomorphism mapping to an internal space of dimension d equipped with a Euclidean metric δIJ. Based on the logic behind this prescription, and armed only with a minimal set of initial assumptions, we will be able to pull off a complete derivation of the dc transport matrix for relativistic field theory (holographic) duals, without the need to fix the Gn’s a priori This part will not be fully developed in terms of an exhaustive analysis, this is a potentially useful result, as universal linear-response features might possibly be extracted from it.
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