Enstrophy from symmetry

We study symmetry principles associated with the approximately conserved enstrophy current, responsible for the inverse energy cascade in non relativistic 2+1 dimensional turbulence. We do so by identifying the accidental symmetry associated with enstrophy current conservation in a recently realized effective action principle for hydrodynamics. Our analysis deals with both relativistic and non relativistic effective actions and their associated symmetries

Testing the membrane paradigm with holography

One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background. We also consider as a concrete example linearized metric perturbations of a five-dimensional AdS-Schwarzschild black brane and show that a spurious excitation appears in the long-wavelength response that is only removed from the spectrum when the membrane paradigm is replaced by ingoing boundary conditions at the event horizon. We interpret this excitation in terms of an additional Goldstone boson that appears due to symmetry breaking by the classical solution ending on the stretched horizon rather than the event horizon.Comment: 5 pages, 1 figure; v2: improved presentation, typos fixed, figure fixed, conclusions unchanged; v3: further improvements in the presentation, conclusions unchanged; v4: shortened, published versio

Unbalanced Holographic Superconductors and Spintronics

We present a minimal holographic model for s-wave superconductivity with unbalanced Fermi mixtures, in 2+1 dimensions at strong coupling. The breaking of a U(1)_A "charge" symmetry is driven by a non-trivial profile for a charged scalar field in a charged asymptotically AdS_4 black hole. The chemical potential imbalance is implemented by turning on the temporal component of a U(1)_B "spin" field under which the scalar field is uncharged. We study the phase diagram of the model and comment on the eventual (non) occurrence of LOFF-like inhomogeneous superconducting phases. Moreover, we study "charge" and "spin" transport, implementing a holographic realization (and a generalization thereof to superconducting setups) of Mott's two-current model which provides the theoretical basis of modern spintronics. Finally we comment on possible string or M-theory embeddings of our model and its higher dimensional generalizations, within consistent Kaluza-Klein truncations and brane-anti brane setups.Comment: 45 pages, 15 figures; v2: two paragraphs below eq. (3.1) slightly modified, figure 5 (left) replaced, references added; v3: typos corrected, comments added, figure 12 replace

A holographic journey from fluids to black holes

Fluid dynamics and gravitational physics are deeply interconnected by means of holography, a recent paradigm stating that any theory of gravity can be equivalently described by a quantum field theory in one dimension less. The last 15 years of research have seen many developments toward a better understanding of such a paradigm which is believed to be a key ingredient for any theory of quantum gravity. Black holes, for instance, can be related to quantum field theories at thermal equilibrium and slightly perturbed black holes are holographically dual to the fluid behaviour of such thermally equilibrated systems. Many questions remain, however, still unanswered, for example how to go beyond the simplest case of Anti-de Sitter gravity, where the best example of holography can be realised; or how to probe physics beyond the black hole horizon etc. Motivated by a better understanding of holography and fluid dynamics, in this thesis i) we successfully construct a holographic dual of the dissipationless effective action for conformal fluids providing a first derivation of such an effective action from first principles. ii) We generalise to a certain extent the procedure of obtaining holographic fluid behaviour from gravity for cases which are not necessarily Anti-de Sitter. iii) We show the differences between holographic fluid behaviour and an older approach to black hole physics going under the name of the membrane paradigm. iv) Finally we show how this membrane paradigm can be used instead as an approximation scheme for neglecting the interior of a black hole and provide its limits of validity

Effective actions for relativistic fluids from holography

Motivated by recent progress in developing action formulations of relativistic hydrodynamics, we use holography to derive the low energy dissipationless effective action for strongly coupled conformal fluids. Our analysis is based on the study of novel double Dirichlet problems for the gravitational field, in which the boundary conditions are set 011 two codimension one flutelike hypersurfaces (branes). We provide a geometric interpretation of the Goldstone bosons appearing in such constructions in terms of a family of spatial geodesics extending between the ultraviolet and the infrared brane. Furthermore, we discuss supplementing double Dirichlet problems with information about the near-horizon geometry. We show that upon coupling to a membrane paradigm boundary condition, our approach reproduces correctly the complex dispersion relation for both sound and shear waves. We also demonstrate that upon a Wick rotation, our formulation reproduces the equilibrium partition function formalism, provided the near- horizon geometry is properly accounted for. Finally, we define the conserved hydrodynamic entropy current as the Noether current associated with a particular transformation of the Goldstone bosons