On the B-twisted topological sigma model and Calabi-Yau geometry

Abstract

We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold is the obstruction to the quantization via Batalin-Vilkovisky formalism. When the first Chern class vanishes, i.e. on Calabi-Yau manifolds, the factorization algebra of observables gives rise to the expected topological correlation functions in the B-model. We explain a twisting procedure to generalize to the Landau-Ginzburg case, and show that the resulting topological correlations coincide with Vafa's residue formula.

73 pages. Comments welcome

References in corpus (4)

• Chiral de Rham complex and the half-twisted sigma-model
• Primitive forms via polyvector fields
• Variation of Hodge structures, Frobenius manifolds and Gauge theory
• Renormalization Method and Mirror Symmetry

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• BV quantization of the Rozansky-Witten model
• Factorization Algebras for Bulk-Boundary Systems
• Lie algebroids as $L_{\infty }$ spaces
• A holography theory of Poisson sigma model and deformation quantization
• Quantizing Derived Mapping Stacks
• Holomorphic field theories and higher algebra