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$_3$, 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