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A survey on mixed spin P-fields. (English) Zbl 1388.14116

This paper is a survey on the theory of mixed spin P-fields, as the title suggests. The authors discuss the problem of the curve counting on the quintic Calabi-Yau threefolds. They recall the construction of the Gromov-Witten invariants of stable maps with P-fields and FJRW 5-spin class constructed as the cosection localised virtual cycle. They also develop a geometric set-up for the phase transition between these two field theories, which is exactly the theory of mixed spin P-fields. They conclude by showing how localisation technique implies relations between the GW and FJRW invariants and allows to compute them in some cases.

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14J81 Relationships between surfaces, higher-dimensional varieties, and physics
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References:

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