Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)

Abstract

In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories by promoting our result to an equivalence of perverse schobers. We prove our equivalence by matching holomorphic Lagrangian skeleta, on the A-model side, with non-commutative resolutions on the B-model side. The hyperkähler geometry of these spaces provides each category with a natural t-structure, which helps clarify SYZ duality in a hyperkähler context. Our results are a prototype for mirror symmetry statements relating pairs of K-theoretic Coulomb branches.

arXiv commentv4: Added Appendix (written with Laurent Côté and Justin Hilburn) describing calculation of homotopy limit of categories; edited discussion of polarizations; other edits throughout

References in corpus (10)

• Mirror Symmetry is T-Duality
• Summing up D-Instantons
• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
• Covariantly functorial wrapped Floer theory on Liouville sectors
• Quasi-Hamiltonian reduction via classical Chern-Simons theory
• Koszul duality patterns in Floer theory
• Mirror symmetry for the Landau-Ginzburg A-model $M={\mathbb{C}}^n,W=z_1\cdots z_n$
• Holomorphic Lagrangian branes correspond to perverse sheaves
• Quantizations of multiplicative hypertoric varieties at a root of unity
• Homological Mirror Symmetry for Hypertoric Varieties I