Orientability for gauge theories on Calabi-Yau manifolds

Abstract

We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing problem in DT theory.

v2: 14 pages, substantially revised and expanded

References in corpus (2)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Derived Algebraic Geometry and Deformation Quantization

Cited by in corpus (25)

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• $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
• Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
• On orientations for gauge-theoretic moduli spaces
• Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
• Stable pair invariants of local Calabi-Yau 4-folds
• Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Perversely categorified Lagrangian correspondences
• Tautological stable pair invariants of Calabi-Yau 4-folds
• Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds
• Counting perverse coherent systems on Calabi-Yau 4-folds
• Counting conics on sextic 4-folds
• Noncommutative Instantons in Diverse Dimensions
• Counting zero-dimensional subschemes in higher dimensions
• A topological approach for emerging D-branes and its implications for gravity
• Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
• Deformation theory of deformed Donaldson-Thomas connections for $\mathrm{Spin}(7)$-manifolds
• Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds
• Mukai flops and Plücker type formulas for hyper-Kähler manifolds