Conformal Complementarity Maps

We study quantum cosmological models for certain classes of bang/crunch singularities, using the duality between expanding bubbles in AdS with a FRW interior cosmology and perturbed CFTs on de Sitter space-time. It is pointed out that horizon complementarity in the AdS bulk geometries is realized as a conformal transformation in the dual deformed CFT. The quantum version of this map is described in full detail in a toy model involving conformal quantum mechanics. In this system the complementarity map acts as an exact duality between eternal and apocalyptic Hamiltonian evolutions. We calculate the commutation relation between the Hamiltonians corresponding to the different frames. It vanishes only on scale invariant states.Comment: 38 pages, 9 figure

Holographic non-computers

We introduce the notion of holographic non-computer as a system which exhibits parametrically large delays in the growth of complexity, as calculated within the Complexity-Action proposal. Some known examples of this behavior include extremal black holes and near-extremal hyperbolic black holes. Generic black holes in higher-dimensional gravity also show non-computing features. Within the $1/d$ expansion of General Relativity, we show that large-$d$ scalings which capture the qualitative features of complexity, such as a linear growth regime and a plateau at exponentially long times, also exhibit an initial computational delay proportional to $d$. While consistent for large AdS black holes, the required `non-computing' scalings are incompatible with thermodynamic stability for Schwarzschild black holes, unless they are tightly caged.Comment: 23 pages, 7 figures. V3: References added. Figures updated. New discussion of small black holes in the canonical ensembl

On the spectrum of nonrelativistic AdS/CFT

We develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrodinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in the holographic direction. We show that most physical requirements, including the introduction of harmonic traps, can be realized with exact AdS metrics, but without any need for exotic matter sectors in the bulk dynamics. This Hamiltonian picture can be used to compare directly with many-body spectra of fermions at unitarity on harmonic traps, thereby providing a direct physical interpretation of the holographic radial coordinate for these systems. Finally, we add some speculations on the dynamical generation of mass gaps in the AdS description, the resulting quasiparticle spectra, and the analog of `deconfining' phase transitions that may occur.Comment: 20 pages and 1 figure; typos corrected, references added; references added, minor changes matching published versio

The Holographic Life of the eta'

In the string holographic dual of large-N_c QCD with N_f flavours of Kruczenski et al, the eta' meson is massless at infinite N_c and dual to a collective fluctuation of N_f D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the generation of a mass of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that the supregravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the theta-angle in the supergravity description occurs only through the combination theta + 2 \sqrt{N_f} eta' / f_pi, as dictated by the U(1) anomaly. We provide a quantitative test by computing the linear term in the eta' potential in two independent ways, with perfect agreement.Comment: 1+26 pages, 8 figures; V4: Appendix added, version published in JHE

Ideal gas matching for thermal Galilean holography

We exhibit a nonrelativistic ideal gas with a Kaluza-Klein tower of species, featuring a singular behavior of thermodynamic functions at zero chemical potential. In this way, we provide a qualitative match to the thermodynamics of recently found black holes in backgrounds with asymptotic nonrelativistic conformal symmetry.Comment: 11 page