A survey on mixed spin P-fields (Q2401750)

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.