854 research outputs found
More Holography from Conformal Field Theory
We extend the work of [4] to support the conjecture that any conformal field
theory with a large N expansion and a large gap in the spectrum of anomalous
dimensions has a local bulk dual. We count to O(1/N^2) the solutions to the
crossing constraints in conformal field theory for a completely general scalar
four-point function and show that, to this order, the counting matches the
number of independent interactions in a general scalar theory on Anti-de Sitter
space. We introduce parity odd conformal blocks for this purpose.Comment: 19 page
Writing CFT correlation functions as AdS scattering amplitudes
We explore the Mellin representation of conformal correlation functions
recently proposed by Mack. Examples in the AdS/CFT context reinforce the
analogy between Mellin amplitudes and scattering amplitudes. We conjecture a
simple formula relating the bulk scattering amplitudes to the asymptotic
behavior of Mellin amplitudes and show that previous results on the flat space
limit of AdS follow from our new formula. We find that the Mellin amplitudes
are particularly useful in the case of conformal gauge theories in the planar
limit. In this case, the four point Mellin amplitudes are meromorphic functions
whose poles and their residues are entirely determined by two and three point
functions of single-trace operators. This makes the Mellin amplitudes the ideal
objects to attempt the conformal bootstrap program in higher dimensions.Comment: 23 pages + appendice
Connecting the Holographic and Wilsonian Renormalization Groups
Inspired by the AdS/CFT correspondence, we develop an explicit formal duality
between the planar limit of a d-dimensional gauge theory and a classical field
theory in a (d+1)-dimensional anti-de Sitter space. The key ingredient is the
identification of fields in AdS with generalized Hubbard-Stratonovich
transforms of single-trace couplings of the QFT. We show that the Wilsonian
renormalization group flow of these transformed couplings matches the
holographic (Hamilton-Jacobi) flow of bulk fields along the radial direction in
AdS. This result allows one to outline an AdS/CFT dictionary that does not rely
on string theory.Comment: 11 pages, 1 figure; metadata modified in v2; added references and
minor changes in v3; v4 as published in JHE
Pensioen wijzigen jegens slapers en pensioengerechtigden
Naar aanleiding van de eerdere publicatie van auteurs inzake 'Wijzigingsvraagstukken in de pensioendriehoek'(TPV 2012/42), is een reactie verschenen van Breuker. In dit artikel wordt gereageer op het artikel van Breuker en verduidelijken auteurs hun standpunt over de juridische (on)houdbaarheid van (1) de uitewerkte rechtsverhouding en (2) pensioenwijzigingen jegens slapers en pensioengerechtigden. De conclusie luidt dat wijziging van opgebouwd pensioen jegens slapers en pensioengerechtigden - inclusief onvoorwaardelijke indexatie - moeilijk is maar wel mogelijk. Een dergelijke wijziging geschiedt onder de Pensioenwet binnen de marges van de wet: via waardeoverdracht of korten. Het door de wetgever gestimuleerde invaren is daar een voorbeeld van. Onder de (voormalige) Pensioen- en Spaarfondsenwet ligt dit anders volgens auteurs. Er gold geen wettelijke beperking ten aanzien van het voorwaardelijk maken van onvoorwaardelijke indexatie. Het pad om de wijzigingen rechtsgeldig door te voeren jegens slapers en pensioengerechtigden is nog steeds hobbelig en onzeker
The holographic quantum effective potential at finite temperature and density
We develop a formalism that allows the computation of the quantum effective
potential of a scalar order parameter in a class of holographic theories at
finite temperature and charge density. The effective potential is a valuable
tool for studying the ground state of the theory, symmetry breaking patterns
and phase transitions. We derive general formulae for the effective potential
and apply them to determine the phase transition temperature and density in the
scaling region.Comment: 27 page
Effective Conformal Theory and the Flat-Space Limit of AdS
We develop the idea of an effective conformal theory describing the low-lying
spectrum of the dilatation operator in a CFT. Such an effective theory is
useful when the spectrum contains a hierarchy in the dimension of operators,
and a small parameter whose role is similar to that of 1/N in a large N gauge
theory. These criteria insure that there is a regime where the dilatation
operator is modified perturbatively. Global AdS is the natural framework for
perturbations of the dilatation operator respecting conformal invariance, much
as Minkowski space naturally describes Lorentz invariant perturbations of the
Hamiltonian. Assuming that the lowest-dimension single-trace operator is a
scalar, O, we consider the anomalous dimensions, gamma(n,l), of the
double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT
we find that perturbative unitarity places a bound on these dimensions of
|gamma(n,l)|<4. Non-renormalizable AdS interactions lead to violations of the
bound at large values of n. We also consider the case that these interactions
are generated by integrating out a heavy scalar field in AdS. We show that the
presence of the heavy field "unitarizes" the growth in the anomalous
dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is
close to the dimension of the CFT operator dual to the heavy field. Finally, we
demonstrate that bulk flat-space S-matrix elements can be extracted from the
large n behavior of the anomalous dimensions. This leads to a direct connection
between the spectrum of anomalous dimensions in d-dimensional CFTs and
flat-space S-matrix elements in d+1 dimensions. We comment on the emergence of
flat-space locality from the CFT perspective.Comment: 46 pages, 2 figures. v2: JHEP published versio
Causality and the AdS Dirichlet problem
The (planar) AdS Dirichlet problem has previously been shown to exhibit
superluminal hydrodynamic sound modes. This problem is defined by bulk
gravitational dynamics with Dirichlet boundary conditions imposed on a rigid
timelike cut-off surface. We undertake a careful examination of this set-up and
argue that, in most cases, the propagation of information between points on the
Dirichlet hypersurface is nevertheless causal with respect to the induced light
cones. In particular, the high-frequency dynamics is causal in this sense.
There are however two exceptions and both involve boundary gravitons whose
propagation is not constrained by the Einstein equations. These occur in i)
AdS, where the boundary gravitons generally do not respect the induced
light cones on the boundary, and ii) Rindler space, where they are related to
the infinite speed of sound in incompressible fluids. We discuss implications
for the fluid/gravity correspondence with rigid Dirichlet boundaries and for
the black hole membrane paradigm.Comment: 29 pages, 5 figures. v2: added refs. v3: minor clarification
Holographic and Wilsonian Renormalization Groups
We develop parallels between the holographic renormalization group in the
bulk and the Wilsonian renormalization group in the dual field theory. Our
philosophy differs from most previous work on the holographic RG; the most
notable feature is the key role of multi-trace operators. We work out the forms
of various single- and double-trace flows. The key question, `what cutoff on
the field theory corresponds to a radial cutoff in the bulk?' is left
unanswered, but by sharpening the analogy between the two sides we identify
possible directions.Comment: 31 pages, 3 figures. v2: Minor clarifications. Added reference
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