A bstract M5 branes probing D-type singularities give rise to 6d (1, 0) SCFTs with SO SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits.

This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture <i></i> (0, <i></i>). So far, a proof was only obtained for apertures <i></i> 0.511. The conviction in the validity of this conjecture for apertures <i></i> 0.511<i></i> mainly relied on numerical computations. In this paper we succeed to prove the existence of bound states for any aperture <i></i> 0.583 using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with computer assistance, we extend this interval up to any aperture <i></i> 0.595<i></i>. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schrdinger operators in the plane with <i></i>-interactions supported on broken lines.

In this paper, we extend our previous work to construct (0, 2) Toda-like mirrors to A/2-twisted theories on more general spaces, as part of a program of understanding (0,2) mirror symmetry. Specifically, we propose (0, 2) mirrors to GLSMs on toric del Pezzo surfaces and Hirzebruch surfaces with deformations of the tangent bundle. We check the results by comparing correlation functions, global symmetries, as well as geometric blowdowns with the corresponding (0, 2) Toda-like mirrors. We also briefly discuss Grassmannian manifolds.

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Let M be a complete Einstein manifold of negative curvature, and assume that (as in the AdS/CFT correspondence) it has a Penrose compactification with a conformal boundary M of positive scalar curvature. We show that under these conditions, M and in particular M must be connected. These results resolve some puzzles concerning the AdS/CFT correspondence.