Open Access
March 2016 On the B-twisted topological sigma model and Calabi–Yau geometry
Qin Li, Si Li
J. Differential Geom. 102(3): 409-484 (March 2016). DOI: 10.4310/jdg/1456754015


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.


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Qin Li. Si Li. "On the B-twisted topological sigma model and Calabi–Yau geometry." J. Differential Geom. 102 (3) 409 - 484, March 2016.


Published: March 2016
First available in Project Euclid: 29 February 2016

zbMATH: 1342.81628
MathSciNet: MR3466804
Digital Object Identifier: 10.4310/jdg/1456754015

Rights: Copyright © 2016 Lehigh University

Vol.102 • No. 3 • March 2016
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