Topological K-theory of quasi-BPS categories for Higgs bundles
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909317802754048 |
|---|---|
| author | Pădurariu, Tudor Toda, Yukinobu |
| author_facet | Pădurariu, Tudor Toda, Yukinobu |
| contents | In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi-BPS categories (called BPS in this case) are non-commutative analogues of Hitchin integrable systems. We proposed a conjectural equivalence between BPS categories which swaps Euler characteristics and weights. The conjecture is inspired by the Dolbeault Geometric Langlands equivalence of Donagi--Pantev, by the Hausel--Thaddeus mirror symmetry, and by the $χ$-independence phenomenon for BPS invariants of curves on Calabi-Yau threefolds.
In this paper, we show that the above conjecture holds at the level of topological K-theories. When the rank and the Euler characteristic are coprime, such an isomorphism was proved by Groechenig--Shen. Along the way, we show that the topological K-theory of BPS categories is isomorphic to the BPS cohomology of the moduli of semistable Higgs bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological K-theory of quasi-BPS categories for Higgs bundles Pădurariu, Tudor Toda, Yukinobu Algebraic Geometry High Energy Physics - Theory Representation Theory In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi-BPS categories (called BPS in this case) are non-commutative analogues of Hitchin integrable systems. We proposed a conjectural equivalence between BPS categories which swaps Euler characteristics and weights. The conjecture is inspired by the Dolbeault Geometric Langlands equivalence of Donagi--Pantev, by the Hausel--Thaddeus mirror symmetry, and by the $χ$-independence phenomenon for BPS invariants of curves on Calabi-Yau threefolds. In this paper, we show that the above conjecture holds at the level of topological K-theories. When the rank and the Euler characteristic are coprime, such an isomorphism was proved by Groechenig--Shen. Along the way, we show that the topological K-theory of BPS categories is isomorphic to the BPS cohomology of the moduli of semistable Higgs bundles. |
| title | Topological K-theory of quasi-BPS categories for Higgs bundles |
| topic | Algebraic Geometry High Energy Physics - Theory Representation Theory |
| url | https://arxiv.org/abs/2409.10800 |