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Mirror manifolds and topological field theory. (English) Zbl 0834.58013
Yau, Shing-Tung (ed.), Essays on mirror manifolds. Cambridge, MA: International Press. 120-159 (1992).
This is a detailed expository paper “devoted to sketching how some of the standard facts relevant to mirror symmetry and its applications can be naturally understood in the context of topological field theory”. On a Calabi-Yau manifold the author introduces two models of topological field theories called \(A\) model and \(B\) model. (Mirror symmetry relates the \(A\) model of one Calabi-Yau manifold to the \(B\) model of its mirror). The further contents of the paper may be seen from the following (partial) list of the section titles: Kähler manifolds and twisted manifolds; reduction to weak coupling; the ghost number anomaly; observables of the \(A\) model; evaluation of the path integrals; anomalies (\(B\)-model); observables (\(B\)-model); correlation functions; the fixed point theorem; relation to the “physical” model; closer look at the observables (both \(A\) and \(B\) models).
For the entire collection see [Zbl 0816.00010].

58D99 Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
81T10 Model quantum field theories
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
32G13 Complex-analytic moduli problems
32J27 Compact Kähler manifolds: generalizations, classification