3D Mirror Symmetry for Instanton Moduli Spaces

Author:

Koroteev PeterORCID,Zeitlin Anton M.

Abstract

AbstractWe prove that the Hilbert scheme of k points on $${\mathbb {C}}^2$$ C 2 ($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ 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 $${\mathbb {C}}^\times _\hbar $$ C ħ × -action. First, we find a two-parameter family $$X_{k,l}$$ X k , l of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of $$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ Hilb k [ C 2 ] is obtained via direct limit $$l\longrightarrow \infty $$ 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 $$\hbar $$ ħ -opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-N sheaves on $${\mathbb {P}}^2$$ P 2 with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual.

Funder

Division of Mathematical Sciences

Simons Foundation

AMS Simons Travel Grant

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Opers on the projective line, Wronskian relations, and the Bethe Ansatz;Journal of Geometry and Physics;2024-08

2. The Zoo of Opers and Dualities;International Mathematics Research Notices;2023-11-28

3. Virtual Coulomb branch and vertex functions;Duke Mathematical Journal;2023-11-15

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3