Super Yang-Mills on Branched Covers and Weighted Projective Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916706868264960 |
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| author | Mauch, Roman Ruggeri, Lorenzo |
| author_facet | Mauch, Roman Ruggeri, Lorenzo |
| contents | In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the $\mathcal{N}=2$ vector multiplet on weighted projective space $\mathbb{CP}^2_{\boldsymbol{N}}$ for equivariant Donaldson-Witten and ``Pestun-like'' theories. We claim that this partition function agrees with the one obtained from dimensional reduction of the 5d $\mathcal{N}=1$ vector multiplet on a certain branched cover of $S^5$. More precisely, the branch locus and indices have to be such that they match the singular locus and deficit angles in $\mathbb{CP}^2_{\boldsymbol{N}}$. Our conjecture is substantiated by checking that partition functions on spindles are similarly obtained from dimensional reduction of the 3d $\mathcal{N}=2$ vector multiplet on branched covers of $S^3$. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Super Yang-Mills on Branched Covers and Weighted Projective Spaces Mauch, Roman Ruggeri, Lorenzo High Energy Physics - Theory In this work we conjecture the Coulomb branch partition function, including flux and instanton contributions, for the $\mathcal{N}=2$ vector multiplet on weighted projective space $\mathbb{CP}^2_{\boldsymbol{N}}$ for equivariant Donaldson-Witten and ``Pestun-like'' theories. We claim that this partition function agrees with the one obtained from dimensional reduction of the 5d $\mathcal{N}=1$ vector multiplet on a certain branched cover of $S^5$. More precisely, the branch locus and indices have to be such that they match the singular locus and deficit angles in $\mathbb{CP}^2_{\boldsymbol{N}}$. Our conjecture is substantiated by checking that partition functions on spindles are similarly obtained from dimensional reduction of the 3d $\mathcal{N}=2$ vector multiplet on branched covers of $S^3$. This work paves the way for obtaining partition functions on more generic symplectic toric orbifolds. |
| title | Super Yang-Mills on Branched Covers and Weighted Projective Spaces |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.11600 |