We develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a “geodesic Witten diagram”, which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.

https://link.springer.com/content/pdf/10.1007%2FJHEP01%282016%29146.pdf

Witten diagrams revisited: the AdS geometry of conformal blocks

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the $(\partial\phi)^4$ coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.

/pdf/causality-constraints-in-conformal-field-theory-2e2izvj6on.pdf

Causality Constraints in Conformal Field Theory

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.

/pdf/causality-constraints-in-conformal-field-theory-uafdqb44y5.pdf

Causality constraints in conformal field theory

We develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram," which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.

/pdf/witten-diagrams-revisited-the-ads-geometry-of-conformal-bce6eh9rq8.pdf

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks

In this work we initiate the conformal bootstrap program for ${\mathcal N}=2$ superconformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of ${\mathcal N}=2$ chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any ${\mathcal N}=2$ superconformal field theory.

/pdf/the-mathcal-n-2-superconformal-bootstrap-42g2aw84vk.pdf

The ${\mathcal N}=2$ superconformal bootstrap

/pdf/generalizable-machine-learning-for-stress-monitoring-from-37h86s1m.pdf

Generalizable machine learning for stress monitoring from wearable devices: A systematic literature review

We study extremal correlation functions of chiral primary operators in the large-N SU(N) ${\cal N} = 2$ superconformal QCD theory and present new results based on supersymmetric localization. We discuss extensively the basis-independent data that can be extracted from these correlators using the leading order large-N matrix model free energy given by the four-sphere partition function. Special emphasis is given to single-trace 2- and 3-point functions as well as a new class of observables that are scalars on the conformal manifold. These new observables are particular quadratic combinations of the structure constants of the chiral ring. At weak 't Hooft coupling we present perturbative results that, in principle, can be extended to arbitrarily high order. We obtain closed-form expressions up to the first subleading order. At strong coupling we provide analogous results based on an approximate Wiener-Hopf method.

/pdf/large-n-correlation-functions-in-cal-n-2-superconformal-qcd-11t4ry5fqw.pdf

Large-N correlation functions in ${\cal N} = 2$ superconformal QCD

Stress monitoring using low-cost electroencephalogram devices: A systematic literature review.

The universal nature of black hole collapse in asymptotically $AdS_3$ gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge $c$. It is known that non-equilibrium states with scaling dimensions of order $c$ can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's equation it is shown that a state that fails to thermalize can be promoted to a thermalizing state by preparing the system beforehand with an energy greater than an appropriate threshold energy. It is generally a difficult problem to ascertain whether a state will thermalize or not. As partial progress to this problem a set of lower bounds are presented for the treshold energy, which can alternatively be interpreted as criteria for thermalization.

/pdf/vacuum-block-thermalization-in-semi-classical-2d-cft-52hnlpfuk6.pdf

Vacuum block thermalization in semi-classical 2d CFT.

Introduction. Wearable sensors have shown promise as a non-intrusive method for collecting biomarkers that may correlate with levels of elevated stress. The stress response has both subjective, psychological and objectively measurable, biological components. Both of them can be expressed differently from person to person, complicating the development of a generic stress measurement model. This is further compounded by the lack of large, labeled datasets that can be utilized to build machine learning models for accurately detecting periods and levels of stress. The datasets publicly available are usually collected using different devices and experimental settings, and are labeled using differing scoring methods. The aim of this review is to provide an overview of the current state of stress detection and monitoring using wearable devices, and where applicable, machine learning techniques utilized. We also shed light on the challenges and opportunities that machine learning-enabled stress monitoring and detection face. Methods. This study reviewed published works contributing and/or using datasets designed for detecting stress and their associated machine learning methods, with a systematic review and meta-analysis of those that utilized wearable sensor data as stress biomarkers. The electronic databases of Google Scholar, Crossref, DOAJ and PubMed were searched for relevant articles and a total of 24 articles were identified and included in the final analysis. The reviewed works were synthesized into three categories of publicly available stress datasets, machine learning, and future research directions. For the machine learning studies reviewed, we provide an analysis of their approach Preprint submitted to Artificial Intelligence in Medicine October 3, 2022 to the different steps of a machine learning development pipeline, further synthesizing the finding and trends in the literature. We also provide a review of several major wearable devices that are able to measure four biomarkers known to be robust indicators of elevated levels of stress. Results. A wide variety of study-specific test and measurement protocols were noted in the literature. A number of public datasets were identified that are labeled for stress detection. We focused mainly on datasets using the Empatica E4 device, a well-studied, easy to access, United States Food and Drug Administration (FDA) approved wrist-worn wearable that provides sensor biomarkers most notable to correlate with elevated levels of stress. Most datasets contain less than twenty-four hours of data, and the varied experimental conditions and labeling methodologies potentially limit their ability to generalize for unseen data. In addition, we discuss that previous works show shortcomings in areas such as their labeling protocols, lack of statistical power, validity of stress biomarkers, and generalization ability. Conclusion. Health tracking and monitoring using wearable devices is growing in popularity, and continued interest with a growing number of studies in this area of health care will likely improve the accuracy of detecting specific health conditions including elevated levels of stress. There is a need for a definitive device-use and setup protocol to enable consistent results across tests with medical-grade wearable devices. Generalization of existing machine learning models still require further study, and research in this area will continue to provide improvements as newer and more substantial datasets become available for study.

Machine Learning for Stress Monitoring from Wearable Devices: A Systematic Literature Review

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