706 research outputs found
Beyond : Gravitational Couplings to Matter and the Stress Tensor OPE
We derive constraints on the operator product expansion of two stress tensors
in conformal field theories (CFTs), both generic and holographic. We point out
that in large CFTs with a large gap to single-trace higher spin operators,
the stress tensor sector is not only universal, but isolated: that is, , where is a single-trace primary. We show
that this follows from a suppression of by powers
of the higher spin gap, , dual to the bulk mass scale of
higher spin particles, and explain why is a more
sensitive probe of than in 4d CFTs. This result
implies that, on the level of cubic couplings, the existence of a consistent
truncation to Einstein gravity is a direct consequence of the absence of higher
spins. By proving similar behavior for other couplings where have spin , we are led to
propose that is the CFT "dual" of an AdS derivative in a
classical action. These results are derived by imposing unitarity on mixed
systems of spinning four-point functions in the Regge limit. Using the same
method, but without imposing a large gap, we derive new inequalities on these
three-point couplings that are valid in any CFT. These are generalizations of
the Hofman-Maldacena conformal collider bounds. By combining the collider bound
on couplings to spin-2 operators with analyticity properties of CFT data,
we argue that all three tensor structures of in the
free-field basis are nonzero in interacting CFTs.Comment: 42+25 pages. v2: added refs, minor change
Unitarity Methods in AdS/CFT
We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams — we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams — in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout
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Privatizing the Metro Card: Transportation Equity in an Open-Loop Smartcard Fare Payment System
The unbanked – individuals who lack a bank account with a mainstream financial institution – are one of the more broadly disadvantaged groups in American society. There is a great deal of demographic overlap between the unbanked as a cohort and other marginalized groups, notably undocumented immigrants, low-income Blacks and Latinos and non-native English speakers. These groups are an important constituency for transportation agencies in that they are more likely to travel by transit than other Americans. As many transit agencies transition their fare payment systems to radio frequency identification (RFID)-based, “contactless” smartcard or open payment technology linked to a rider’s bank account, there are growing opportunities to enhance multi-modalism in passenger trips, reduce operations costs, increase system profitability, and expand access to fare payment media. However, due to equity requirements of the Civil Rights Act, transit agencies must ensure that the smartcard technology also accommodates the unbanked. Ensuring that transit fare payment systems adequately serve the unbanked requires an assessment of New York’s unbanked population beyond that which is available in current academic literature. A 2011 study from the NYC Department of Consumer Affairs identified several New York City neighborhoods with the highest proportions of unbanked and underbanked residents. Through intercept surveys in two of these majority-unbanked neighborhoods – Fordham (Bronx) and Bushwick (Brooklyn) – this study attempts to clarify the travel behavior and fare payment characteristics of the un(der)banked. In addition, this study investigates potential fare policy alternatives in an open payment system that would adequately accommodate the transportation needs of the unbanked. To articulate policy recommendations to meet this objective, this study includes structured interviews with transit fare policy experts in the public, private and nonprofit sectors. These interviews explored how transit agencies can select the most appropriate fare payment technology; effectively partner with retailers and alternative financial services (AFS) to make its new fare payment medium accessible to un(der)banked communities; and establish performance metrics to monitor the fare payment system’s long-term equity
-dimensional SYK, AdS Loops, and Symbols
We study the symbol for the conformal group, and its appearance in three
seemingly unrelated contexts: the SYK model, conformal representation theory,
and perturbative amplitudes in AdS. The contribution of the planar Feynman
diagrams to the three-point function of the bilinear singlets in SYK is shown
to be a symbol. We generalize the computation of these and other Feynman
diagrams to dimensions. The symbol can be viewed as the crossing
kernel for conformal partial waves, which may be computed using the Lorentzian
inversion formula. We provide closed-form expressions for symbols in
. In AdS, we show that the symbol is the Lorentzian inversion of
a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging
the double-trace OPE data. Finally, we consider one-loop diagrams in AdS with
internal scalars and external spinning operators, and show that the triangle
diagram is a symbol, while one-loop -gon diagrams are built out of
symbols.Comment: 62 pages; v2 fixed typos and references, added comments about
anomalous dimensions; v3, fixed typos, published versio
The Conformal Bootstrap at Finite Temperature
We initiate an approach to constraining conformal field theory (CFT) data at
finite temperature using methods inspired by the conformal bootstrap for vacuum
correlation functions. We focus on thermal one- and two-point functions of
local operators on the plane. The KMS condition for thermal two-point functions
is cast as a crossing equation. By studying the analyticity properties of
thermal two-point functions, we derive a "thermal inversion formula" whose
output is the set of thermal one-point functions for all operators appearing in
a given OPE. This involves identifying a kinematic regime which is the analog
of the Regge regime for four-point functions. We demonstrate the effectiveness
of the inversion formula by recovering the spectrum and thermal one-point
functions in mean field theory, and computing thermal one-point functions for
all higher-spin currents in the critical model at leading order in
. Furthermore, we develop a systematic perturbation theory for thermal
data in the large spin, low-twist spectrum of any CFT. We explain how the
inversion formula and KMS condition may be combined to algorithmically
constrain CFTs at finite temperature. Throughout, we draw analogies to the
bootstrap for vacuum four-point functions. Finally, we discuss future
directions for the thermal conformal bootstrap program, emphasizing
applications to various types of CFTs, including those with holographic duals.Comment: 59 pages plus appendices, 14 figures. v2: added refs, minor
correction
Unitarity Methods in AdS/CFT
We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams — we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams — in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout
On the growth of linear perturbations
We consider the linear growth of matter perturbations in various dark energy
(DE) models. We show the existence of a constraint valid at between the
background and dark energy parameters and the matter perturbations growth
parameters. For CDM lies in a
very narrow interval for . Models with a constant equation of state inside General
Relativity (GR) are characterized by a quasi-constant , for
for example we have while
can have a nonnegligible variation. A smoothly varying equation of
state inside GR does not produce either . A measurement of
on small redshifts could help discriminate between various DE
models even if their is close, a possibility interesting for DE
models outside GR for which a significant can be obtained.Comment: 8 pages, 8 figures. Results unchanged; clarifying sentence added; one
reference adde
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