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3D Mirror Symmetry for Instanton Moduli Spaces.
- Source :
-
Communications in Mathematical Physics . Oct2023, Vol. 403 Issue 2, p1005-1068. 64p. - Publication Year :
- 2023
-
Abstract
- We prove that the Hilbert scheme of k points on C 2 ( Hilb k [ C 2 ] ) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the C ħ × -action. First, we find a two-parameter family X k , l of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of Hilb k [ C 2 ] is obtained via direct limit l ⟶ ∞ and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted ħ -opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-N sheaves on P 2 with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MIRROR symmetry
*K-theory
*SHEAF theory
*ALGEBRA
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 403
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 172330882
- Full Text :
- https://doi.org/10.1007/s00220-023-04831-5