Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe

Preference uncertainty accounts for developmental effects on susceptibility to peer influence in adolescence.

Adolescents are prone to social influence from peers, with implications for development, both adaptive and maladaptive. Here, using a computer-based paradigm, we replicate a cross-sectional effect of more susceptibility to peer influence in a large dataset of adolescents 14 to 24 years old. Crucially, we extend this finding by adopting a longitudinal perspective, showing that a within-person susceptibility to social influence decreases over a 1.5 year follow-up time period. Exploiting this longitudinal design, we show that susceptibility to social influences at baseline predicts an improvement in peer relations over the follow-up period. Using a Bayesian computational model, we demonstrate that in younger adolescents a greater tendency to adopt others' preferences arises out of a higher uncertainty about their own preferences in the paradigmatic case of delay discounting (a phenomenon called 'preference uncertainty'). This preference uncertainty decreases over time and, in turn, leads to a reduced susceptibility of one's own behaviour to an influence from others. Neuro-developmentally, we show that a measure of myelination within medial prefrontal cortex, estimated at baseline, predicts a developmental decrease in preference uncertainty at follow-up. Thus, using computational and neural evidence, we reveal adaptive mechanisms underpinning susceptibility to social influence during adolescence

Simplifying instanton corrections to N=4 SYM correlators

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Gauge-invariant correlation functions in light-cone superspace

We initiate a study of correlation functions of gauge-invariant operators in N=4 super Yang-Mills theory using the light-cone superspace formalism. Our primary aim is to develop efficient methods to compute perturbative corrections to correlation functions. This analysis also allows us to examine potential subtleties which may arise when calculating off-shell quantities in light-cone gauge. We comment on the intriguing possibility that the manifest N=4 supersymmetry in this approach may allow for a compact description of entire multiplets and their correlation functions.Comment: 35 pages, several figure

Experience-based VAS values for EQ-5D-3L health states in a national general population health survey in China

Purpose: To investigate the feasibility of deriving experience-based visual analogue scale (VAS) values for EQ-5D-3L health states using national general population health survey data in China. Methods: The EQ-5D-3L was included in the National Health Services Survey (n = 120,709, aged 15–103 years) to measure health-related quality of life. The respondents reported their current health status on a VAS and completed the EQ-5D-3L questionnaire, enabling modelling of the association between the experience-based VAS values and self-reported problems on EQ-5D dimensions and severity levels. Results: VAS values were generally negatively associated with problems reported on the EQ-5D dimensions, and the anxiety/depression dimension had the greatest impact on VAS values. A previously obtained value for dead allowed the values for all 243 EQ-5D-3L health states to be transformed to the 0–1 scale (0 = dead, 1 = full health). Conclusions: This study presents the feasibility of deriving an experience-based VAS values for EQ-5D-3L health states in China. The analysis of these VAS data raises more fundamental issues concerning the universal nature of the classification system and the extent to which Chinese respondents utilise the same concepts of health as defined by this classification system

Rigid Supersymmetric Theories in Curved Superspace

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For $\mathcal{M}=AdS_4$ we reproduce the known results in the literature. A supersymmetric Lagrangian for $\mathcal{M}=\mathbb{S}^4$ exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for $\mathcal{M}=\mathbb{S}^3\times \mathbb{R}$ and note that the time direction $\mathbb{R}$ can be rotated to Euclidean signature and be compactified to $\S^1$ only when the theory has a continuous R-symmetry. The partition function on $\mathcal{M}=\mathbb{S}^3\times \S^1$ is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant $\mathcal{N}=2$ theories on $\mathbb{S}^3$ and clarify a few points about them.Comment: 26 pages, uses harvmac; v2 with added reference

Exploring Curved Superspace

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that M is locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change

Patient and public involvement: how much do we spend and what are the benefits?

BACKGROUND AND OBJECTIVES: Patient and public involvement (PPI) is seen as a way of helping to shape health policy and ensure a patient-focused health-care system. While evidence indicates that PPI can improve health-care decision making, it also consumes monetary and non-monetary resources. Given the financial climate, it is important to start thinking about the costs and benefits of PPI and how to evaluate it in economic terms. DESIGN: We conducted a literature review to assess the potential benefits and costs of involvement and the challenges in carrying out an economic evaluation of PPI. RESULTS: The benefits of PPI include effects on the design of new projects or services, on NHS governance, on research design and implementation and on citizenship and equity. Economic evaluation of PPI activities is limited. The lack of an appropriate analytical framework, data recording and understanding of the potential costs and benefits of PPI, especially from participants' perspectives, represent serious constraints on the full evaluation of PPI. CONCLUSIONS: By recognizing the value of PPI, health-care providers and commissioners can embed it more effectively within their organizations. Better knowledge of costs may prompt organizations to effectively plan, execute, evaluate and target resources. This should increase the likelihood of more meaningful activity, avoid tokenism and enhance organizational efficiency and reputation

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 adde