1,347 research outputs found
AdS Field Theory from Conformal Field Theory
We provide necessary and sufficient conditions for a Conformal Field Theory
to have a description in terms of a perturbative Effective Field Theory in AdS.
The first two conditions are well-known: the existence of a perturbative `1/N'
expansion and an approximate Fock space of states generated by a finite number
of low-dimension operators. We add a third condition, that the Mellin
amplitudes of the CFT correlators must be well-approximated by functions that
are bounded by a polynomial at infinity in Mellin space, or in other words,
that the Mellin amplitudes have an effective theory-type expansion. We explain
the relationship between our conditions and unitarity, and provide an analogy
with scattering amplitudes that becomes exact in the flat space limit of AdS.
The analysis also yields a simple connection between conformal blocks and AdS
diagrams, providing a new calculational tool very much in the spirit of the
S-Matrix program.
We also begin to explore the potential pathologies associated with higher
spin fields in AdS by generalizing Weinberg's soft theorems to AdS/CFT. The AdS
analog of Weinberg's argument constrains the interactions of conserved currents
in CFTs, but there are potential loopholes that are unavailable to theories of
massless higher spin particles in flat spacetime.Comment: 31+7 pages, 5 figure
Unitarity and the Holographic S-Matrix
The bulk S-Matrix can be given a non-perturbative definition in terms of the
flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the
optical theorem, can be derived by studying the behavior of the OPE and the
conformal block decomposition in the flat space limit. When applied to
perturbation theory in AdS, this gives a holographic derivation of the cutting
rules for Feynman diagrams.
To demonstrate these facts we introduce some new techniques for the analysis
of conformal field theories. Chief among these is a method for conglomerating
local primary operators to extract the contribution of an individual primary in
their OPE. This provides a method for isolating the contribution of specific
conformal blocks which we use to prove an important relation between certain
conformal block coefficients and anomalous dimensions. These techniques make
essential use of the simplifications that occur when CFT correlators are
expressed in terms of a Mellin amplitude.Comment: 33+12 pages, 6 figures; v2: typos corrected, some clarifications
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Bounds on OPE coefficients in 4D Conformal Field Theories
We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension and extend previous studies of bounds on OPE coefficients of conserved vector currents to the product groups SO(N)
7SO(M). We also analyze the bounds on the OPE coefficients of the conserved vector currents associated with the groups SO(N), SU(N) and SO(N)
7SO(M) under the assumption that in the singlet channel no scalar operator has dimension less than four, namely that the CFT has no relevant deformations. This is motivated by applications in the context of composite Higgs models, where the strongly coupled sector is assumed to be a spontaneously broken CFT with a global symmetry. \ua9 The Authors
Analyticity and the Holographic S-Matrix
We derive a simple relation between the Mellin amplitude for AdS/CFT
correlation functions and the bulk S-Matrix in the flat spacetime limit,
proving a conjecture of Penedones. As a consequence of the Operator Product
Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic
function with simple poles on the real axis. This provides a powerful and
suggestive handle on the locality vis-a-vis analyticity properties of the
S-Matrix. We begin to explore analyticity by showing how the familiar poles and
branch cuts of scattering amplitudes arise from the holographic description.
For this purpose we compute examples of Mellin amplitudes corresponding to
1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime
limit of conformal blocks, implicitly relating the S-Matrix program to the
Bootstrap program for CFTs. We use this connection to show how the existence of
small black holes in AdS leads to a universal prediction for the conformal
block decomposition of the dual CFT.Comment: 28+15 pages, 7 figures; v2: typos correcte
Seed conformal blocks in 4D CFT
We compute in closed analytical form the minimal set of \u201cseed\u201d conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (\u2113, \u2113) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, |\u2113 12 \u2113|) and one (|\u2113 12 \u2113|, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (\u2113, \u2113), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = |\u2113 12 \u2113| and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories
New insights into single-molecule junctions using a robust, unsupervised approach to data collection and analysis
We have applied a new, robust and
unsupervised approach to data
collection, sorting and analysis that provides fresh insights into
the nature of single-molecule junctions. Automation of tunneling current-distance
(<i>I</i>(<i>s</i>)) spectroscopy facilitates
the collection of very large data sets (up to 100 000 traces
for a single experiment), enabling comprehensive statistical interrogations
with respect to underlying tunneling characteristics, noise and junction
formation probability (JFP). We frequently observe unusual low-to-high
through-molecule conductance features with increasing electrode separation,
in addition to numerous other “plateau” shapes, which
may be related to changes in interfacial or molecular bridge structure.
Furthermore, for the first time we use the JFP to characterize the
homogeneity of functionalized surfaces at the nanoscale
On Feynman rules for Mellin amplitudes in AdS/CFT
The computation of CFT correlation functions via Witten diagrams in AdS space
can be simplified via the Mellin transform. Recently a set of Feynman rules for
tree-level Mellin space amplitudes has been proposed for scalar theories. In
this note we derive these rules by explicitly evaluating all of the relevant
Witten diagram integrals for the scalar phi^n theory. We also check that the
rules reduce to the usual Feynman rules in the flat space limit.Comment: minor corrections, published versio
Mellin Amplitudes for Dual Conformal Integrals
Motivated by recent work on the utility of Mellin space for representing
conformal correlators in /CFT, we study its suitability for representing
dual conformal integrals of the type which appear in perturbative scattering
amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for
writing Mellin amplitudes for a large class of integrals in any dimension, and
find explicit representations for several familiar toy integrals. However we
show that the power of Mellin space is that it provides simple representations
even for fully massive integrals, which except for the single case of the
4-mass box have not yet been computed by any available technology. Mellin space
is also useful for exhibiting differential relations between various multi-loop
integrals, and we show that certain higher-loop integrals may be written as
integral operators acting on the fully massive scalar -gon in
dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very
simple formula expressing the 6-mass double box as a single integral of the
6-mass scalar hexagon in 6 dimensions.Comment: 29+7 page
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