Structure constants of operators on the Wilson loop from integrability

We study structure constants of local operators inserted on the Wilson loop in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in the SU(2) sector at tree level using the correspondence between operators on the Wilson loop and the open spin chain. The results are interpreted as the summation over all possible ways of changing the signs of magnon momenta in the hexagon form factors. This is consistent with a holographic description of the correlator as the cubic open string vertex, which consists of one hexagonal patch and three boundaries. We then conjecture that a similar expression should hold also at finite coupling.Comment: 38 pages; v3: JHEP published versio

Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.Comment: 31 pages + appendices; v2 References adde

Personal customizing exercise with a wearable measurement and control unit

BACKGROUND: Recently, wearable technology has been used in various health-related fields to develop advanced monitoring solutions. However, the monitoring function alone cannot meet all the requirements of customizing machine-based exercise on an individual basis by relying on biosignal-based controls. We propose a new wearable unit design equipped with measurement and control functions to support the customization process. METHODS: The wearable unit can measure the heart rate and electromyogram signals during exercise performance and output workload control commands to the exercise machines. The workload is continuously tracked with exercise programs set according to personally customized workload patterns and estimation results from the measured biosignals by a fuzzy control method. Exercise programs are adapted by relying on a computer workstation, which communicates with the wearable unit via wireless connections. A prototype of the wearable unit was tested together with an Internet-based cycle ergometer system to demonstrate that it is possible to customize exercise on an individual basis. RESULTS: We tested the wearable unit in nine people to assess its suitability to control cycle ergometer exercise. The results confirmed that the unit could successfully control the ergometer workload and continuously support gradual changes in physical activities. CONCLUSION: The design of wearable units equipped with measurement and control functions is an important step towards establishing a convenient and continuously supported wellness environment

Correlation functions on the Half-BPS Wilson loop: perturbation and hexagonalization

Abstract We compute correlation functions of protected primaries on the 1/2-BPS Wilson loop in N = 4 $$\mathcal{N}=4$$ super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201 . We then analyze the results in view of the integrability-based approach called “hexagonalization”, which was introduced previously to study the correlation functions in the absence of the Wilson loop. In this approach, one decomposes the correlator into fundamental building blocks called “hexagons”, and glues them back together by summing over the intermediate states. Through the comparison, we conjecture that the correlation functions on the Wilson loop can be computed by contracting hexagons with boundary states, where each boundary state represents a segment of the Wilson loop. As a byproduct, we make predictions for the large-charge asymptotics of the structure constants on the Wilson loop. Along the way, we refine the conjecture for the integrability-based approach to the general non-BPS structure constants on the Wilson loop, proposed originally in arXiv:1706.02989