Abstract:We extend the recent work on fluid-gravity correspondence to charged blackbranes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.
The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. In this article, we study a Galilean fluid with a conserved Uð1Þ current up to anomalies. We construct a relativistic system, which we call a null fluid and show that it is in one-to-one correspondence with a Galilean fluid living in one lower dimension. The correspondence is based on light cone reduction, which is known to reduce the Poincaré symmetry of a theory to Galilean in one lower dimension. We show that the proposed null fluid and the corresponding Galilean fluid have exactly same symmetries, thermodynamics, constitutive relations, and equilibrium partition to all orders in the derivative expansion. We also devise a mechanism to introduce Uð1Þ anomaly in even dimensional Galilean theories using light cone reduction, and study its effect on the constitutive relations of a Galilean fluid.
The dynamics of finite temperature U(N ) gauge theories on S 3 can be described, at weak coupling, by an effective unitary matrix model. Here we present an exact solution to these models, for any value of N , in terms of a sum over representations. Taking the large N limit of this solution provides a new perspective on the deconfinement transition which is supposed to be dual to the Hawking-Page transition. The large N phase transition manifests itself here in a manner similar to the Douglas-Kazakov phase transition in 2d Yang-Mills theory. We carry out a complete analysis of the saddle representation in the simplest case involving only the order parameter TrU . We find that the saddle points corresponding to thermal AdS, the small black hole and the large black hole can all be described in terms of free fermions. They all admit a simple phase space description a la the BPS geometries of Lin, Lunin and Maldacena.
Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution is closely linked to the universal anomaly induced transport coefficients in hydrodynamics which have been studied before using entropy techniques. Equilibrium partition function provides an alternate and a microscopically more transparent way to derive the constraints on these transport coefficients. We re-derive this way all the known results on these transport coefficients including their polynomial structure which has recently been conjectured to be linked to the anomaly polynomial of the theory. Further we link the local description of anomaly induced transport in terms of a Gibbs current to the more global description in terms of the partition function.
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