Bow varieties: Stable envelopes and their 3d mirror symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910694588284928 |
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| author | Botta, Tommaso Maria Rimanyi, Richard |
| author_facet | Botta, Tommaso Maria Rimanyi, Richard |
| contents | In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of holomorphic symplectic varieties$\unicode{x2013}$called Cherkis bow varieties$\unicode{x2013}$their elliptic stable envelopes exhibit a duality property inspired by mirror symmetry in $d=3$, $\mathcal N=4$ quantum field theories. A crucial step of our proof involves the process of ''resolving'' large charge branes into multiple smaller charge branes. This phenomenon turns out to be the geometric counterpart of the algebraic fusion procedure. Along the way we discover various new features in the geometry of bow varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07300 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bow varieties: Stable envelopes and their 3d mirror symmetry Botta, Tommaso Maria Rimanyi, Richard Algebraic Geometry Mathematical Physics Quantum Algebra Representation Theory 55N34, 81T30, 14J33, 20G42, 14C17 In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of holomorphic symplectic varieties$\unicode{x2013}$called Cherkis bow varieties$\unicode{x2013}$their elliptic stable envelopes exhibit a duality property inspired by mirror symmetry in $d=3$, $\mathcal N=4$ quantum field theories. A crucial step of our proof involves the process of ''resolving'' large charge branes into multiple smaller charge branes. This phenomenon turns out to be the geometric counterpart of the algebraic fusion procedure. Along the way we discover various new features in the geometry of bow varieties. |
| title | Bow varieties: Stable envelopes and their 3d mirror symmetry |
| topic | Algebraic Geometry Mathematical Physics Quantum Algebra Representation Theory 55N34, 81T30, 14J33, 20G42, 14C17 |
| url | https://arxiv.org/abs/2308.07300 |