195 research outputs found
Singleton field theory and Flato - Fronsdal dipole equation
We study solutions of the equations and
in global coordinates on the covering space
of the -dimensional Anti de-Sitter space subject to various
boundary conditions and their connection to the unitary irreducible
representations of . The ``vanishing flux'' boundary
conditions at spatial infinity lead to the standard quantization scheme for
in which solutions of the second- and the fourth-order equations are
equivalent. To include fields realizing the singleton unitary representation in
the bulk of one has to relax the boundary conditions thus allowing for
the nontrivial space of solutions of the dipole equation known as the Gupta -
Bleuler triplet. We obtain explicit expressions for the modes of the Gupta -
Bleuler triplet and the corresponding two-point function.
To avoid negative-energy states one must also introduce an additional
constraint in the space of solutions of the dipole equation.Comment: 25 pages, 2 figures; significant change
Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study
the effects of curvature-squared terms in the dual gravity action on transport
coefficients, quasinormal spectra and the analytic structure of thermal
correlators at strong coupling. To understand the behavior and possible
pathologies of the Gauss-Bonnet fluid in dimensions, we compute
(analytically and non-perturbatively in the Gauss-Bonnet coupling) its
second-order transport coefficients, the retarded two- and three-point
correlation functions of the energy-momentum tensor in the hydrodynamic regime
as well as the relevant quasinormal spectrum. The Haack-Yarom universal
relation among the second-order transport coefficients is violated at second
order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the
holographic fluid still produces entropy, while the momentum diffusion and the
sound attenuation are suppressed at all orders in the hydrodynamic expansion.
By adding higher-derivative electromagnetic field terms to the action, we also
compute corrections to charge diffusion and identify the non-perturbative
parameter regime in which the charge diffusion constant vanishes.Comment: 56 pages, 3 figures; V2: references added, version published in JHE
From strong to weak coupling in holographic models of thermalization
We investigate the analytic structure of thermal energy-momentum tensor
correlators at large but finite coupling in quantum field theories with gravity
duals. We compute corrections to the quasinormal spectra of black branes due to
the presence of higher derivative and terms in the action, focusing
on the dual to SYM theory and Gauss-Bonnet gravity. We observe
the appearance of new poles in the complex frequency plane at finite coupling.
The new poles interfere with hydrodynamic poles of the correlators leading to
the breakdown of hydrodynamic description at a coupling-dependent critical
value of the wave-vector. The dependence of the critical wave vector on the
coupling implies that the range of validity of the hydrodynamic description
increases monotonically with the coupling. The behavior of the quasinormal
spectrum at large but finite coupling may be contrasted with the known
properties of the hierarchy of relaxation times determined by the spectrum of a
linearized kinetic operator at weak coupling. We find that the ratio of a
transport coefficient such as viscosity to the relaxation time determined by
the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the
vicinity of infinite coupling but flattens out for weaker coupling, suggesting
an extrapolation from strong coupling to the kinetic theory result. We note
that the behavior of the quasinormal spectrum is qualitatively different
depending on whether the ratio of shear viscosity to entropy density is greater
or less than the universal, infinite coupling value of . In the
former case, the density of poles increases, indicating a formation of branch
cuts in the weak coupling limit, and the spectral function shows the appearance
of narrow peaks. We also discuss the relation of the viscosity-entropy ratio to
conjectured bounds on relaxation time in quantum systems.Comment: V2: 53 pages, 31 figures. References adde
The complex life of hydrodynamic modes
We study analytic properties of the dispersion relations in classical
hydrodynamics by treating them as Puiseux series in complex momentum. The radii
of convergence of the series are determined by the critical points of the
associated complex spectral curves. For theories that admit a dual
gravitational description through holography, the critical points correspond to
level-crossings in the quasinormal spectrum of the dual black hole. We
illustrate these methods in supersymmetric Yang-Mills theory in
3+1 dimensions, in a holographic model with broken translation symmetry in 2+1
dimensions, and in conformal field theory in 1+1 dimensions. We comment on the
pole-skipping phenomenon in thermal correlation functions, and show that it is
not specific to energy density correlations.Comment: V3: 54 pages, 18 figures. Appendix added. Version to appear in JHE
On the convergence of the gradient expansion in hydrodynamics
Hydrodynamic excitations corresponding to sound and shear modes in fluids are
characterised by gapless dispersion relations. In the hydrodynamic gradient
expansion, their frequencies are represented by power series in spatial
momenta. We investigate the analytic structure and convergence properties of
the hydrodynamic series by studying the associated spectral curve in the space
of complexified frequency and complexified spatial momentum. For the strongly
coupled supersymmetric Yang-Mills plasma, we use the holographic
duality methods to demonstrate that the derivative expansions have finite
non-zero radii of convergence. Obstruction to the convergence of hydrodynamic
series arises from level-crossings in the quasinormal spectrum at complex
momenta.Comment: V3: 5 pages, 2 figures. Final version. Published in Physical Review
Letters with the title "Convergence of the Gradient Expansion in
Hydrodynamics
RG Fixed Points in Supergravity Duals of 4-d Field Theory and Asymptotically AdS Spaces
Recently, it has been conjectured that supergravity solutions with two asymptotically AdS regions describe the RG flow of a 4-d field theory from a UV fixed point to an interacting IR fixed point. In this paper we lend support to this conjecture by showing that, in the UV (IR) limit, the two-point function of a minimally-coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS_5. This result is consistent with the interpretation of the radial coordinate of Anti de Sitter space as an energy scale, and it may provide an analog of the Callan-Symanzik equation for supergravity duals of strongly coupled field theories
Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes
In holography, quasinormal spectra of black branes coincide with the poles of
retarded finite-temperature correlation functions of a dual quantum field
theory in the limit of infinite number of relevant degrees of freedom such as
colours. For asymptotically anti-de Sitter backgrounds, the spectra form a
characteristic pattern in the complex frequency plane, colloquially known as
the "Christmas tree". At infinite coupling, the tree has only one pair of
branches. At large but finite coupling, the branches become more dense and lift
up towards the real axis, consistent with the expectation of forming a branch
cut in the limit of zero coupling. However, it is known that at zero coupling,
the corresponding correlators generically have not one but multiple branch cuts
separated by intervals proportional to the Matsubara frequency. This suggests
the existence of multiple branches of the "Christmas tree" spectrum in dual
gravity. In this note, we show numerically how these additional branches of the
spectrum can emerge from the dual gravitational action with higher-derivative
terms. This phenomenon appears to be robust, yet, reproducing the expected weak
coupling behaviour of the correlators quantitatively implies the existence of
certain constraints on the coefficients of the higher-derivative terms of the
dual gravity theory.Comment: V2: 13 pages, 8 figures. Version to appear in JHE
- …