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.

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 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 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 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.

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.

Background: To more accurately quantify the potential impact of the neighbourhood environment on adults’ physical activity (PA), it is important to compare environment-PA associations between periods of the day or week when adults are more versus less likely to be in their neighbourhood and utilise its PA resources. We examined whether, among adults from 10 countries, associations between objectively-assessed neighbourhood environment attributes and moderate-to-vigorous physical activity (MVPA) varied by time of the day and day of the week. The secondary aim was to examine whether such associations varied by employment status, gender and city.

Methods: This cross-sectional study included 6,712 adults from 14 cities across 10 countries with ≥1 day of valid accelerometer-assessed MVPA and complete information on socio-demographic and objectively-assessed environmental characteristics within 0.5 and 1 km street-network buffers around the home. Accelerometer measures (MVPA min/h) were created for six time periods from early morning until late evening/night, for weekdays and weekend days separately. Associations were estimated using generalized additive mixed models.

Results: Time of the day, day of week, gender and employment status were significant moderators of environment-MVPA associations. Land use mix was positively associated with MVPA in women who were employed and in men irrespective of their employment status. The positive associations between MVPA and net residential density, intersection density and land use mix were stronger in the mornings of weekdays and the afternoon/evening periods of both weekdays and weekend days. Associations between number of parks and MVPA were stronger in the mornings and afternoon/evenings irrespective of day of the week. Public transport density showed consistent positive associations with MVPA during weekends, while stronger effects on weekdays were observed in the morning and early evenings.

Conclusions: This study suggests that space and time constraints in adults’ daily activities are important factors that determine the impact of neighbourhood attributes on PA. Consideration of time-specific associations is important to better characterise the magnitude of the effects of the neighbourhood environment on PA. Future research will need to examine the contribution of built environment characteristics of areas surrounding other types of daily life centres (e.g., workplaces) to explaining adults’ PA at specific times of the day.

Background: Emerging interventions that rely on and harness variability in behavior to adapt to individual performance over time may outperform interventions that prescribe static goals (e.g., 10,000 steps/day). The purpose of this factorial trial was to compare adaptive vs. static goal setting and immediate vs. delayed, non-contingent financial rewards for increasing free-living physical activity (PA).

Methods: A 4-month 2 × 2 factorial randomized controlled trial tested main effects for goal setting (adaptive vs. static goals) and rewards (immediate vs. delayed) and interactions between factors to increase steps/day as measured by a Fitbit Zip. Moderate-to-vigorous PA (MVPA) minutes/day was examined as a secondary outcome.

Results: Participants (N = 96) were mainly female (77%), aged 41 ± 9.5 years, and all were insufficiently active and overweight/obese (mean BMI = 34.1 ± 6.2). Participants across all groups increased by 2389 steps/day on average from baseline to intervention phase (p < .001). Participants receiving static goals showed a stronger increase in steps per day from baseline phase to intervention phase (2630 steps/day) than those receiving adaptive goals (2149 steps/day; difference = 482 steps/day, p = .095). Participants receiving immediate rewards showed stronger improvement (2762 step/day increase) from baseline to intervention phase than those receiving delayed rewards (2016 steps/day increase; difference = 746 steps/day, p = .009). However, the adaptive goals group showed a slower decrease in steps/day from the beginning of the intervention phase to the end of the intervention phase (i.e. less than half the rate) compared to the static goals group (−7.7 steps vs. -18.3 steps each day; difference = 10.7 steps/day, p < .001) resulting in better improvements for the adaptive goals group by study end. Rate of change over the intervention phase did not differ between reward groups. Significant goal phase x goal setting x reward interactions were observed.

Conclusions: Adaptive goals outperformed static goals (i.e., 10,000 steps) over a 4-month period. Small immediate rewards outperformed larger, delayed rewards. Adaptive goals with either immediate or delayed rewards should be preferred for promoting PA.

In this paper we study the four-point correlation function of the energy–momentum supermultiplet in theories with N = 4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N = 4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N = 4 super Yang–Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.