Calabi-Yau Deformation Quantization

2026/07/28 by Jakob Ulmer
#math.QA #hep-th #math.AG #math.AT

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Abstract

We record the Calabi-Yau version of Kontsevich's formality morphism from deformation quantization. As a special case we find that any unimodular holomorphic Poisson Calabi-Yau has a canonical closed deformation quantization of its resolved algebra of functions. A broader motivation is to find an explanation of Kontsevich's deformation quantization in the setting of Calabi-Yau categories via Sen-Zwiebach's string vertices.

Citations

• Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
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• Topological conformal field theories and Calabi-Yau categories
• Homological Algebra of Mirror Symmetry

Related

• Deformation Quantisation via Kontsevich Formality Theorem
• Lectures on Deformation quantization of Poisson manifolds
• Kontsevich's deformation quantization: from Dirac to multiple zeta values
• Deformation Quantization on ℝ^d
• Deformations of algebras in noncommutative geometry