Super Macdonald polynomials and BPS state counting on the blow-up
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918149486542848 |
|---|---|
| author | Kanno, Hiroaki Ohkawa, Ryo Shiraishi, Jun'ichi |
| author_facet | Kanno, Hiroaki Ohkawa, Ryo Shiraishi, Jun'ichi |
| contents | We explore the relation of the super Macdonald polynomials and the BPS state counting on the blow-up of $\mathbb{P}^2$, which is mathematically described by framed stable perverse coherent sheaves. Fixed points of the torus action on the moduli space of BPS states are labeled by super partitions. From the equivariant character of the tangent space at the fixed points we can define the Nekrasov factor for a pair of super partitions, which is used for the localization computation of the partition function. The Nekrasov factor also allows us to compute matrix elements of the action of the quantum toroidal algebra of type $\mathfrak{gl}_{1|1}$ on the $K$ group of the moduli space. We confirm that these matrix elements are consistent with the Pieri rule of the super Macdonald polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Super Macdonald polynomials and BPS state counting on the blow-up Kanno, Hiroaki Ohkawa, Ryo Shiraishi, Jun'ichi High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory We explore the relation of the super Macdonald polynomials and the BPS state counting on the blow-up of $\mathbb{P}^2$, which is mathematically described by framed stable perverse coherent sheaves. Fixed points of the torus action on the moduli space of BPS states are labeled by super partitions. From the equivariant character of the tangent space at the fixed points we can define the Nekrasov factor for a pair of super partitions, which is used for the localization computation of the partition function. The Nekrasov factor also allows us to compute matrix elements of the action of the quantum toroidal algebra of type $\mathfrak{gl}_{1|1}$ on the $K$ group of the moduli space. We confirm that these matrix elements are consistent with the Pieri rule of the super Macdonald polynomials. |
| title | Super Macdonald polynomials and BPS state counting on the blow-up |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2506.01415 |