5 problems

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The hypercomplex manifold HKT or bi-HKT conjecture
Hypercomplex HKT or bi-HKT conjecture. Any hypercomplex manifold is either HKT or bi-HKT.
Conjectureopenhkt-geometry hypercomplex-geometry supersymmetric-sigma-modelsarXiv posted 2 days ago
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Sevrin–Troost conjecture on general $d4a9=(2,2)$ sigma models
Two-dimensional sigma models with $d4a9=(2,2)$ supersymmetry may involve standard chiral, twisted chiral, and semi-chiral multiplets. Sevrin–Troost conjecture. Most general sigma m…
Conjectureopensuperspace supersymmetric-sigma-models supersymmetryarXiv posted 2 days ago
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FIS conjecture on linear harmonic constraints for N=4 HKT models
The model is an ${\cal N}=4$ HKT sigma model formulated in harmonic superspace in terms of original $q^{+}$ superfields. A linear harmonic constraint is a harmonic-superspace const…
Conjectureopenharmonic-superspace hkt-geometry supersymmetric-sigma-modelsarXiv posted 2 days ago
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The nonlinear multiplet conjecture for bi-HKT and bi-Kähler geometries
Nonlinear multiplet conjecture. Models described by nonlinear multiplets describe bi-HKT and bi-Kähler manifolds, but with nonzero Obata connections.
Conjectureopenhkt-geometry kahler-geometry supersymmetric-sigma-modelsarXiv posted 2 days ago
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The converse conjecture for Obata-flat HKT manifolds and linear multiplets
Converse conjecture. Every Obata-flat HKT manifold can be described with linear $({\bf 4},{\bf 4},{\bf 0})$ multiplets.
Conjectureopenhkt-geometry supersymmetric-sigma-modelsarXiv posted 2 days ago

5 problems

The hypercomplex manifold HKT or bi-HKT conjecture

Sevrin–Troost conjecture on general d4a9=(2,2)d4a9=(2,2)d4a9=(2,2) sigma models

FIS conjecture on linear harmonic constraints for N=4 HKT models

The nonlinear multiplet conjecture for bi-HKT and bi-Kähler geometries

The converse conjecture for Obata-flat HKT manifolds and linear multiplets

Sevrin–Troost conjecture on general $d4a9=(2,2)$ sigma models