60 research outputs found
Shear Modes, Criticality and Extremal Black Holes
We consider a (2+1)-dimensional field theory, assumed to be holographically
dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and
calculate the retarded correlators of charge (vector) current and
energy-momentum (tensor) operators at finite momentum and frequency. We show
that, similar to what was observed previously for the correlators of scalar and
spinor operators, these correlators exhibit emergent scaling behavior at low
frequency. We numerically compute the electromagnetic and gravitational
quasinormal frequencies (in the shear channel) of the extremal
Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in
the retarded correlators. The picture that emerges is quite simple: there is a
branch cut along the negative imaginary frequency axis, and a series of
isolated poles corresponding to damped excitations. All of these poles are
always in the lower half complex frequency plane, indicating stability. We show
that this analytic structure can be understood as the proper limit of finite
temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference
Non-Equilibrium Field Dynamics of an Honest Holographic Superconductor
Most holographic models of superconducting systems neglect the effects of
dynamical boundary gauge fields during the process of spontaneous
symmetry-breaking. Usually a global symmetry gets broken. This yields a
superfluid, which then is gauged "weakly" afterwards. In this work we build
(and probe the dynamics of) a holographic model in which a local boundary
symmetry is spontaneously broken instead. We compute two-point functions of
dynamical non-Abelian gauge fields in the normal and in the broken phase, and
find non-trivial gapless modes. Our AdS3 gravity dual realizes a p-wave
superconductor in (1+1) dimensions. The ground state of this model also breaks
(1+1)-dimensional parity spontaneously, while the Hamiltonian is
parity-invariant. We discuss possible implications of our results for a wider
class of holographic liquids.Comment: 32 pages, 12 figures; v3: string theory derivation of setup added
(section 3.1), improved presentation, version accepted by JHEP; v2: paragraph
added to discussion, figure added, references added, typos correcte
Transport in holographic superfluids
We construct a slowly varying space-time dependent holographic superfluid and
compute its transport coefficients. Our solution is presented as a series
expansion in inverse powers of the charge of the order parameter. We find that
the shear viscosity associated with the motion of the condensate vanishes. The
diffusion coefficient of the superfluid is continuous across the phase
transition while its third bulk viscosity is found to diverge at the critical
temperature. As was previously shown, the ratio of the shear viscosity of the
normal component to the entropy density is 1/(4 pi). As a consequence of our
analysis we obtain an analytic expression for the backreacted metric near the
phase transition for a particular type of holographic superfluid.Comment: 45 pages + appendice
Parity-Violating Hydrodynamics in 2+1 Dimensions
We study relativistic hydrodynamics of normal fluids in two spatial
dimensions. When the microscopic theory breaks parity, extra transport
coefficients appear in the hydrodynamic regime, including the Hall viscosity,
and the anomalous Hall conductivity. In this work we classify all the transport
coefficients in first order hydrodynamics. We then use properties of response
functions and the positivity of entropy production to restrict the possible
coefficients in the constitutive relations. All the parity-breaking transport
coefficients are dissipationless, and some of them are related to the
thermodynamic response to an external magnetic field and to vorticity. In
addition, we give a holographic example of a strongly interacting relativistic
fluid where the parity-violating transport coefficients are computable.Comment: 39+1 page
Quasinormal modes and holographic correlators in a crunching AdS geometry
We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable supersymmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a `square', and the exact holographic correlators display striking similarities to their counterparts in the BTZ black hole and its higher dimensional generalisations. We numerically determine quasinormal poles for relevant and irrelevant operators, and find an intricate pattern of these in the complex frequency plane. In the case of relevant operators, the deformation parameter has an infinite sequence of critical values, each one characterised by a pair of poles colliding and moving away from the imaginary frequency axis with increasing deformation. In the limit of infinite deformation all scalar operators have identical quasinormal spectra. We compare and contrast our strongly coupled de Sitter QFT results with strongly coupled thermal correlators from AdS black holes
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