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The planar integrability of $\mathcal{N}=4$ super-Yang-Mills (SYM) is the cornerstone for numerous exact observables. We show that the large charge sector of the ${\rm SU}(2)$ $\mathcal{N}=4$ SYM provides another interesting solvable corner which exhibits striking similarities despite being far from the planar limit. We study non-BPS operators obtained by small deformations of half-BPS operators with $R$-charge $J$ in the limit $J\to\infty$ with $\lambda_{J}\equiv g_{\rm YM}^2 J/2$ fixed. The dynamics in this {\it large charge 't Hooft limit} is constrained by a centrally-extended $\mathfrak{psu}(2|2)^2$ symmetry that played a crucial role for the planar integrability. To the leading order in $1/J$, the spectrum is fully fixed by this symmetry, manifesting the magnon dispersion relation familiar from the planar limit, while it is constrained up to a few constants at the next order. We also determine the structure constant of two large charge operators and the Konishi operator, revealing a rich structure interpolating between the perturbative series at weak coupling and the worldline instantons at strong coupling. In addition we compute heavy-heavy-light-light (HHLL) four-point functions of half-BPS operators in terms of resummed conformal integrals and recast them into an integral form reminiscent of the hexagon formalism in the planar limit. For general ${\rm SU}(N)$ gauge groups, we study integrated HHLL correlators by supersymmetric localization and identify a dual matrix model of size $J/2$ that reproduces our large charge result at $N=2$. Finally we discuss a relation to the physics on the Coulomb branch and explain how the dilaton Ward identity emerges from a limit of the conformal block expansion. We comment on generalizations including the large spin 't Hooft limit, the combined large $N$-large $J$ limits, and applications to general $\mathcal{N}=2$ superconformal field theories., Comment: 120 pages

We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS$_2$ geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS$_2$ black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS$_2$ string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to $SL(2,\mathbb{R})$ invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in ${\cal N}=4$ SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling., Comment: 66 + 21 pages, 4 figures; v2 Added figures 2, 3, and 5, clarified discussions in section 3 and section 6.3, and made additional minor edits. Results unchanged

We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several light insertions in the double-scaling limit where the 't Hooft coupling $\lambda$ and the large charge $J$ are sent to infinity, with the ratio $J/\sqrt{\lambda}$ held fixed. They are holographically dual to the expectation values of light vertex operators on a classical string solution with large angular momentum, which we evaluate in the leading large $J$ limit. We also compute the two-point function of large charge insertions by evaluating the on-shell string action, supplemented by the boundary terms that generalize the one introduced by Drukker, Gross and Ooguri for the Wilson loop without insertions. For a special class of correlation functions, we reproduce the string results from field theory by using supersymmetric localization. The results are given by correlation functions in an "emergent" matrix model whose matrix size is proportional to $J$ and whose spectral curve coincides with that of the classical string. Similar matrix models appeared in the study of extremal correlators in rank-1 $\mathcal{N}=2$ superconformal field theories, but our results hold also for non-extremal cases., Comment: 60 pages, 6 figures; v2: footnote 4 edited, reference added

Social and professional networks affect labor market dynamics, knowledge diffusion and new business creation. To understand the determinants of how these networks are formed in the first place, we analyze a unique dataset of business cards exchanges among a sample of over 240,000 users of the multi-platform contact management and professional social networking tool for individuals Eight. We develop a structural model of network formation with strategic interactions, and we estimate users' payoffs that depend on the composition of business relationships, as well as indirect business interactions. We allow heterogeneity of users in both observable and unobservable characteristics to affect how relationships form and are maintained. The model's stationary equilibrium delivers a likelihood that is a mixture of exponential random graph models that we can characterize in closed-form. We overcome several econometric and computational challenges in estimation, by exploiting a two-step estimation procedure, variational approximations and minorization-maximization methods. Our algorithm is scalable, highly parallelizable and makes efficient use of computer memory to allow estimation in massive networks. We show that users payoffs display homophily in several dimensions, e.g. location; furthermore, users unobservable characteristics also display homophily., This version employs Uber's H3 index to measure geospatial homophily. Higher number of iterations are used for the EM algorithm. We evaluate convergence of the lower bound, and evaluate the impact of including covariates information for block recovery compared to when this information is not used. We open sourced the library employed for this research and include a link to the repository

Meeting future global staple crop demand requires continual productivity improvement. Many performance indicators have been proposed to track and measure the increase in productivity while minimizing environmental degradation. However, their use has lagged behind theory, and has not been uniform across crops in different geographies. The consequence is an uneven understanding of opportunities for sustainable intensification. Simple but robust key performance indicators (KPIs) are needed to standardize knowledge across crops and geographies. This paper defines a new term ‘agronomic gain’ based on an improvement in KPIs, including productivity, resource use efficiencies, and soil health that a specific single or combination of agronomic practices delivers under certain environmental conditions. We apply the concept of agronomic gain to the different stages of science-based agronomic innovations and provide a description of different approaches used to assess agronomic gain including yield gap assessment, meta-data analysis, on-station and on-farm studies, impact assessment, panel studies, and use of subnational and national statistics for assessing KPIs at different stages. We mainly focus on studies on rice in sub-Saharan Africa, where large yield gaps exist. Rice is one of the most important staple food crops and plays an essential role in food security in this region. Our analysis identifies major challenges in the assessment of agronomic gain, including differentiating agronomic gain from genetic gain, unreliable in-person interviews, and assessment of some KPIs at a larger scale. To overcome these challenges, we suggest to (i) conduct multi-environment trials for assessing variety × agronomic practice × environment interaction on KPIs, and (ii) develop novel approaches for assessing KPIs, through development of indirect methods using remote-sensing technology, mobile devices for systematized site characterization, and establishment of empirical relationships among KPIs or between agronomic practices and KPIs., Field Crops Research, 270, ISSN:0378-4290, ISSN:1872-6852

The four dimensional N=4 super-Yang-Mills (SYM) theory exhibits rich dynamics in the presence of codimension-one conformal defects. The new structure constants of the extended operator algebra consist of one-point functions of local operators which are nonvanishing due to the defect insertion and carry nontrivial coupling dependence. We study an important class of half-BPS superconformal defects engineered by D5 branes that share three common directions with the D3 branes and involve Nahm pole configurations for the SYM fields on the D3 brane worldvolume. In the planar large N limit, we obtain non-perturbative results in the 't Hooft coupling λ for the defect one-point functions of both BPS and non-BPS operators, building upon recent progress in localization [1] and integrability methods [2,3].For BPS operator insertions in the SYM with D5-brane type boundary or interface, we derive an effective two dimensional defect-Yang-Mills (dYM) theory from supersymmetric localization, which gives an efficient way to extract defect observables and generates a novel matrix model for the defect one-point function. By solving the matrix model in the large N limit, we obtain exact results in λ which interpolate between perturbative Feynman diagram contributions in the weak coupling limit and IIB string theory predictions on AdS5×S5 in the strong coupling regime, providing a precision test of AdS/CFT with interface defects. For general non-BPS operators, we develop a non-perturbative bootstrap-type program for integrable boundary states on the worldsheet of the IIB string theory, corresponding to the interface defects in the planar SYM. Such integrable boundary states are constrained by a set of general consistency conditions for which we present explicit solutions that reproduce and extend the known results at weak coupling from integrable spin-chain methods.

Physical review letters 121(23), 231602 (2018). doi:10.1103/PhysRevLett.121.231602, We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_c$ genus expansion and at any order in the ’t Hooft coupling $g_{YM}^{2}N_c$. In this multistep proposal, one polygonizes the string world sheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a nonplanar four-point correlator of large 1/2 Bogomol’nyi-Prasad-Sommerfield operators at one and two loops., Published by APS, College Park, Md.

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators inN ¼ 4 supersymmetric Yang-Mills theory at higher orders in the large Nc genus expansion and at any order in the ’t Hooft coupling g2 YMNc. In this multistep proposal, one polygonizes the string world sheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator.We test our integrability-based conjecture against a nonplanar four-point correlator of large 1/2 Bogomol’nyi-Prasad-Sommerfield operators at one and two loops.

We introduce a non-perturbative framework for computing structure constants of single-trace operators in the N=4 SYM theory at large N. Our approach features new vertices, with hexagonal shape, that can be patched together into three- and possibly higher-point correlators. These newborn hexagons are more elementary and easier to deal with than the three-point functions. Moreover, they can be entirely constructed using integrability, by means of a suitable bootstrap program. In this letter, we present our main results and conjectures for these vertices, and match their predictions for the three-point functions with both weak and strong coupling data available in the literature., 13 pages + several appendices