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Predictions for Gromov-Witten invariants of noncommutative resolutions. (English) Zbl 1321.14041

The author demonstrates a calculation of the GLSM for \(\mathbb{P}^7[2,2,2,2]\) by using the localization method of [H.Jockers et al., Commun. Math. Phys. 325, No. 3, 1139-1170 (2014; Zbl 1301.81253)]. At the nonlinear sigma model phase, the calculation recovers the Gromov-Witten invariants of \(\mathbb{P}^7[2,2,2,2]\). By applying the same method to the Landau-Ginzburg phase, the author makes a prediction for Gromov-Witten invariants of the noncommutative resolution of the branched double cover, which is the Landau-Ginzburg point of the GLSM. The author finds that the results do not match with the Gromov-Witten invariants of a smooth branched double cover and concludes that they are not related by complex structure deformation in the SCFT moduli space.

MSC:

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Citations:

Zbl 1301.81253
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References:

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