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Topological orbifold models and quantum cohomology rings. (English) Zbl 0795.53074
The topological sigma model on an orbifold target space is investigated. The author describes the moduli space of classical minima for computing correlation functions involving twisted operators, and shows, through a detailed computation of an orbifold of \(\mathbb{C} \mathbb{P}^ 1\) by the dihedral group \(D_ 4\), how to compute the complete ring of observables. Using this procedure, all the rings of dihedral \(\mathbb{C} \mathbb{P}^ 1\) orbifolds are computed. Then, considering \(\mathbb{C} \mathbb{P}^ 2/D_ 4\), it is shown how the techniques of topological – anti-topological fusion might be used for computing twist field correlation functions for non-Abelian orbifolds.

MSC:
53Z05 Applications of differential geometry to physics
81T70 Quantization in field theory; cohomological methods
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