ASU Scholarship Showcase

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a nontrivial analytic continuation which, in the framework of CFT, can be performed elegantly in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N = 4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N = 4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N = 4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N = 4SYM that should be valid at any coupling and away from the planar limit.

The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.

We address the near-collinear expansion of NMHV six-particle scattering amplitudes at strong value of the 't Hooft coupling in planar maximally supersymmetric Yang–Mills theory. We complement recent studies of this observable within the context of the Pentagon Operator Product Expansion, via the dual superWilson loop description, by studying effects of multiple scalar exchanges that accompany (or not) massive flux-tube excitations. Due to the fact that holes have a very small, nonperturbatively generated mass m_h which is exponentially suppressed in the 't Hooft coupling, their exchanges must be resummed in the ultraviolet limit, T <<1/m_h. This procedure yields a contribution to the expectation value of the superloop which enters on equal footing with the classical area — a phenomenon which was earlier observed for MHV amplitudes. In all components, the near-massless scalar exchanges factorize from the ones of massive particles, at leading order in strong coupling.

Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twist-two contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for flux-tube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respect to the R-symmetry group and provide solutions to them to all orders in 't Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to four-loop order.

We address the near-collinear expansion of multiparticle NMHV amplitudes, namely, the heptagon and octagons in the dual language of null polygonal super Wilson loops. In particular, we verify multiparticle factorization of charged pentagon transitions in terms of pentagons for single flux-tube excitations within the framework of refined operator product expansion. We find a perfect agreement with available tree and one-loop data.

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.

We compute one-loop renormalization group equations for non-singlet twist-four operators in QCD. The calculation heavily relies on the light-cone gauge formalism in the momentum fraction space that essentially rephrases the analysis of all two-to-two and two-to-three transition kernels to purely algebraic manipulations both for non- and quasipartonic operators. This is the first brute force calculation of this sector available in the literature. Fourier transforming our findings to the coordinate space, we checked them against available results obtained within a conformal symmetry-based formalism that bypasses explicit diagrammatic calculations and confirmed agreement with the latter.

Background: Many studies used the older ActiGraph (7164) for physical activity measurement, but this model has been replaced with newer ones (e.g., GT3X+). The assumption that new generation models are more accurate has been questioned, especially for measuring lower intensity levels. The low-frequency extension (LFE) increases the low-intensity sensitivity of newer models, but its comparability with older models is unknown. This study compared step counts and physical activity collected with the 7164 and GT3X + using the Normal Filter and the LFE (GT3X+N and GT3X+LFE, respectively).

Findings: Twenty-five adults wore 2 accelerometer models simultaneously for 3Âdays and were instructed to engage in typical behaviors. Average daily step counts and minutes per day in nonwear, sedentary, light, moderate, and vigorous activity were calculated. Repeated measures ANOVAs with post-hoc pairwise comparisons were used to compare mean values. Means for the GT3X+N and 7164 were significantly different in 4 of the 6 categories (p < .05). The GT3X+N showed 2041 fewer steps per day and more sedentary, less light, and less moderate than the 7164 (+25.6, -31.2, -2.9 mins/day, respectively). The GT3X+LFE showed non-significant differences in 5 of 6 categories but recorded significantly more steps (+3597 steps/day; p < .001) than the 7164.

Conclusion: Studies using the newer ActiGraphs should employ the LFE for greater sensitivity to lower intensity activity and more comparable activity results with studies using the older models. Newer generation ActiGraphs do not produce comparable step counts to the older generation devices with the Normal filter or the LFE.

Background: Advancements in geographic information systems over the past two decades have increased the specificity by which an individual’s neighborhood environment may be spatially defined for physical activity and health research. This study investigated how different types of street network buffering methods compared in measuring a set of commonly used built environment measures (BEMs) and tested their performance on associations with physical activity outcomes.

Methods: An internationally-developed set of objective BEMs using three different spatial buffering techniques were used to evaluate the relative differences in resulting explanatory power on self-reported physical activity outcomes. BEMs were developed in five countries using ‘sausage,’ ‘detailed-trimmed,’ and ‘detailed,’ network buffers at a distance of 1 km around participant household addresses (n = 5883).

Results: BEM values were significantly different (p < 0.05) for 96% of sausage versus detailed-trimmed buffer comparisons and 89% of sausage versus detailed network buffer comparisons. Results showed that BEM coefficients in physical activity models did not differ significantly across buffering methods, and in most cases BEM associations with physical activity outcomes had the same level of statistical significance across buffer types. However, BEM coefficients differed in significance for 9% of the sausage versus detailed models, which may warrant further investigation.

Conclusions: Results of this study inform the selection of spatial buffering methods to estimate physical activity outcomes using an internationally consistent set of BEMs. Using three different network-based buffering methods, the findings indicate significant variation among BEM values, however associations with physical activity outcomes were similar across each buffering technique. The study advances knowledge by presenting consistently assessed relationships between three different network buffer types and utilitarian travel, sedentary behavior, and leisure-oriented physical activity outcomes.

Background: The World Health Organization recommends strategies to improve urban design, public transportation, and recreation facilities to facilitate physical activity for non-communicable disease prevention for an increasingly urbanized global population. Most evidence supporting environmental associations with physical activity comes from single countries or regions with limited variation in urban form. This paper documents variation in comparable built environment features across countries from diverse regions.

Methods: The International Physical Activity and the Environment Network (IPEN) study of adults aimed to measure the full range of variation in the built environment using geographic information systems (GIS) across 12 countries on 5 continents. Investigators in Australia, Belgium, Brazil, Colombia, the Czech Republic, Denmark, China, Mexico, New Zealand, Spain, the United Kingdom, and the United States followed a common research protocol to develop internationally comparable measures. Using detailed instructions, GIS-based measures included features such as walkability (i.e., residential density, street connectivity, mix of land uses), and access to public transit, parks, and private recreation facilities around each participant’s residential address using 1-km and 500-m street network buffers.

Results: Eleven of 12 countries and 15 cities had objective GIS data on built environment features. We observed a 38-fold difference in median residential densities, a 5-fold difference in median intersection densities and an 18-fold difference in median park densities. Hong Kong had the highest and North Shore, New Zealand had the lowest median walkability index values, representing a difference of 9 standard deviations in GIS-measured walkability.

Conclusions: Results show that comparable measures can be created across a range of cultural settings revealing profound global differences in urban form relevant to physical activity. These measures allow cities to be ranked more precisely than previously possible. The highly variable measures of urban form will be used to explain individuals’ physical activity, sedentary behaviors, body mass index, and other health outcomes on an international basis. Present measures provide the ability to estimate dose–response relationships from projected changes to the built environment that would otherwise be impossible.