Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917529517031424 |
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| author | Ruggeri, Lorenzo |
| author_facet | Ruggeri, Lorenzo |
| contents | We compute the contour integral for the partition function of an $\mathcal{N}=2$ $SU(2)$ topologically twisted theory on $\mathbb{CP}^2$, dimensionally reducing from an $\mathcal{N}=1$ theory on $S^5$. Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of $\mathbb{CP}^2$. Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of $\mathbb{CP}^2$, which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over $\mathbb{CP}^2$ appear intrinsically via the dimensional reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes Ruggeri, Lorenzo High Energy Physics - Theory We compute the contour integral for the partition function of an $\mathcal{N}=2$ $SU(2)$ topologically twisted theory on $\mathbb{CP}^2$, dimensionally reducing from an $\mathcal{N}=1$ theory on $S^5$. Earlier works presented the partition function as a sum over three equivariant fluxes, one for each toric divisor of $\mathbb{CP}^2$. Our result depends only on a single physical flux, assigned to the non-trivial two-cycle of the manifold. The reduced summation over fluxes is compensated by a contour of integration, arising from a different solution of the BPS equations, which captures more poles in each topological sector. As our observable involves a position-dependent Yang-Mills coupling, we compute new equivariant invariants of $\mathbb{CP}^2$, which reduce to Donaldson invariants in the non-equivariant limit. Stability conditions of gauge bundles over $\mathbb{CP}^2$ appear intrinsically via the dimensional reduction. |
| title | Contour Integral for the Partition Function of $\mathcal{N}=2$ Topologically Twisted on $\mathbb{CP}^2$ and Physical Fluxes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.27526 |