Quantisation via Branes and Minimal Resolution
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910680865570816 |
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| author | Qiu, Jian |
| author_facet | Qiu, Jian |
| contents | The `brane quantisation' is a quantisation procedure developed by Gukov and Witten \cite{Gukov:2008ve}.
We implement this idea by combining it with the tilting theory and the minimal resolutions. This way, we can realistically compute the deformation quantisation on the space of observables acting on the Hilbert space. We apply this procedure to certain quantisation problems in the context of generalised Kähler structure on $\mathbb{P}^2$. Our approach differs from and complements that of Bischoff and Gualtieri \cite{Bischoff:2021ixy}.
We also benefitted from an important technical tool: a combinatorial criterion for the Maurer-Cartan equation, developed in \cite{BarmeierWang} by Barmeier and Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06792 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantisation via Branes and Minimal Resolution Qiu, Jian High Energy Physics - Theory Algebraic Geometry Symplectic Geometry The `brane quantisation' is a quantisation procedure developed by Gukov and Witten \cite{Gukov:2008ve}. We implement this idea by combining it with the tilting theory and the minimal resolutions. This way, we can realistically compute the deformation quantisation on the space of observables acting on the Hilbert space. We apply this procedure to certain quantisation problems in the context of generalised Kähler structure on $\mathbb{P}^2$. Our approach differs from and complements that of Bischoff and Gualtieri \cite{Bischoff:2021ixy}. We also benefitted from an important technical tool: a combinatorial criterion for the Maurer-Cartan equation, developed in \cite{BarmeierWang} by Barmeier and Wang. |
| title | Quantisation via Branes and Minimal Resolution |
| topic | High Energy Physics - Theory Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2304.06792 |