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In this work, we present a reproducible suite of test problems for large-scale optimization (“inverse design” and “topology optimization”) in photonics, where the prevalence of irregular, non-intuitive geometries can otherwise make it challenging to be confident that new algorithms and software are functioning as claimed. We include test problems that exercise a wide array of physical and mathematical features—far-field metalenses, 2d and 3d mode converters, resonant emission and focusing, and dispersion/eigenvalue engineering—and introduce ana posteriorilengthscale metric for comparing designs produced by disparate algorithms. For each problem, we incorporate cross-checks against multiple independent software packages and algorithms, and reproducible designs and their validations scripts are included. We believe that this suite should make it much easier to develop, validate, and gain trust in future inverse-design approaches and software.

 

A bstract The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS 2 × S 2 and AdS 2 × S 4 worldvolume geometries, ending at the AdS 5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q -functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.