Broad vanishing conjecture for cosection-localized GLSM virtual classes

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Let XX be a GLSM target, let Xct⊂XX^{\mathrm{ct}}\subset X be the zero section, and let Zg,n,βϵZ^{\epsilon}_{g,n,\beta} be the relevant moduli space with cosection-localized virtual class. For ϕ∈HCR∗(X)\phi\in H^*_{\mathrm{CR}}(X) satisfying

e\bigl(T_{\overline{\mathcal{I}}X/\overline{\mathcal{I}}X^{\mathrm{ct}}\bigr)\phi=0,

where ee denotes the Euler class, consider the evaluation maps ev⁡i\operatorname{ev}_i.

Broad vanishing conjecture. For every i∈{1,…,n}i\in\{1,\ldots,n\},

ev⁡i∗(ϕ)∩[Zg,n,βϵ]vir=0.\operatorname{ev}_i^*(\phi)\cap[Z^{\epsilon}_{g,n,\beta}]^{\mathrm{vir}}=0.

This vanishing is intended to prove independence of correlators from the choice of lifts to the extended state space. The supplied source gives no resolution status for the conjecture.

References

Primary source

Emily Clader, Felix Janda and Yongbin Ruan, “Higher-genus wall-crossing in the gauged linear sigma model”, arXiv:1706.05038 (2018).

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