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

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

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

Short-cut to new anomalies in gravity duals to logarithmic conformal field theories

Various massive gravity theories in three dimensions are conjecturally dual to logarithmic conformal field theories (LCFTs). We summarise the status of these conjectures. LCFTs are characterised by the values of the central charges and the so-called "new anomalies". We employ a short-cut to calculate these new anomalies in generalised massive gravity and in the recently proposed higher-derivative gravity theories with holographic c-theorem. Both cases permit LCFTs exhibiting intriguing features, like rank three Jordan cells or non-zero central charges. Finally, as an example we discuss in some detail the partially massless version of new massive gravity, a theory with several special properties that we call "partially massless gravity".Comment: 34 pages, 2 figures; v2: added references; v3: Several rewordings in the introduction and section 2, added references. Matches published versio

Introducing the composite time trade-off: a test of feasibility and face validity

__Abstract__ __Introduction__ This study was designed to test the feasibility and face validity of the composite time trade-off (composite TTO), a new approach to TTO allowing for a more consistent elicitation of negative health state values. __Methods__ The new instrument combines a conventional TTO to elicit values for states regarded better than dead and a lead-time TTO for states worse than dead. __Results__ A total of 121 participants completed the composite TTO for ten EQ-5D-5L health states. Mean values ranged from −0.104 for health state 53555 to 0.946 for 21111. The instructions were clear to 98 % of the respondents, and 95 % found the task easy to understand, indicating feasibility. Further, the average number of steps taken in the iteration procedure to achieve the point of indifference in the TTO and the average duration of each task were indicative of a deliberate cognitive process. __Conclusion__ Face validity was confirmed by the high mean values for the mild health states (>0.90) and low mean values for the severe states (<0.42). In conclusion, this study demonstrates the feasibility and face validity of the composite TTO in a face-to-face standardized computer-assisted interview setting

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

The episodic random utility model unifies time trade-off and discrete choice approaches in health state valuation

ABSTRACT: BACKGROUND: To present an episodic random utility model that unifies time trade-off and discrete choice approaches in health state valuation. METHODS: First, we introduce two alternative random utility models (RUMs) for health preferences: the episodic RUM and the more common instant RUM. For the interpretation of time trade-off (TTO) responses, we show that the episodic model implies a coefficient estimator, and the instant model implies a mean slope estimator. Secondly, we demonstrate these estimators and the differences between the estimates for 42 health states using TTO responses from the seminal Measurement and Valuation in Health (MVH) study conducted in the United Kingdom. Mean slopes are estimates with and without Dolan's transformation of worse-than-death (WTD) responses. Finally, we demonstrate an exploded probit estimator, an extension of the coefficient estimator for discrete choice data that accommodates both TTO and rank responses. RESULTS: By construction, mean slopes are less than or equal to coefficients, because slopes are fractions and, therefore, magnify downward errors in WTD responses. The Dolan transformation of WTD responses causes mean slopes to increase in similarity to coefficient estimates, yet they are not equivalent (i.e., absolute mean difference = 0.179). Unlike mean slopes, coefficient estimates demonstrate strong concordance with rank-based predictions (Lin's rho = 0.91). Combining TTO and rank responses under the exploded probit model improves the identification of health state values, decreasing the average width of confidence intervals from 0.057 to 0.041 compared to TTO only results. CONCLUSION: The episodic RUM expands upon the theo