Hydrodynamic Vortices and their Gravity Duals

In this talk we review analytical and numerical studies of hydrodynamic vortices in conformal fluids and their gravity duals. We present two conclusions. First, (3+1)-dimensional turbulence is within the range of validity of the AdS/hydrodynamics correspondence. Second, the local equilibrium of the fluid is equivalent to the ultralocality of the holographic correspondence, in the sense that the bulk data at a given point is determined, to any given precision, by the boundary data at a single point together with a fixed number of derivatives. With this criterion we see that the cores of hot and slow (3+1)-dimensional conformal generalizations of Burgers vortices are everywhere in local equilibrium and their gravity duals are thus easily found. On the other hand local equilibrium breaks down in the core of singular (2+1)-dimensional vortices, but the holographic correspondence with Einstein gravity may be used to define the boundary field theory in the region in which the hydrodynamic description fails.Comment: 6 pages, Padova Strings proceedings to appear in Fortschritte der Physi

Spiked Monopoles

We introduce the spiked monopole, which is a 't Hooft-Polyakov monopole with two charged scalar Higgs fields, of which one enjoys a quartic self-interaction. The free Higgs field behaves as in a BPS monopole, reducing the inter-monopole repulsion. The other Higgs has a spiked profile similar to a non-BPS monopole. Using the methods from numerical relativity recently adapted to the Yang-Mills-Higgs theory by Vachaspati, we simulate the interactions of such monopoles. During the long lifetime of these simulations the individual monopoles are stable. We find that they are always repulsive, with a small repulsion only when the interaction Higgs VEV is proportionately small. We briefly comment on implications for giant monopole dark matter models and on supermassive black hole seeding by the spikes.Comment: 18 pages, 4 PDF figure