From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
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| Format: | Preprint |
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2023
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| _version_ | 1866915332014211072 |
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| author | Lundin, Jim Mauch, Roman Ruggeri, Lorenzo |
| author_facet | Lundin, Jim Mauch, Roman Ruggeri, Lorenzo |
| contents | We compute the Coulomb branch partition function of the 4d $\mathcal{N}=2$ vector multiplet on closed simply-connected quasi-toric manifolds $B$. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is to obtain flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $\mathcal{N}=1$ vector multiplet on closed simply-connected toric Sasaki-manifolds $M$ which are principal $S^1$-bundles over $B$. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients $M/\mathbb{Z}_h$ along the $S^1$, the locus picks up non-trivial flat connections which, in the limit $h\to\infty$, provide the sought-after fluxes on $B$. We compute the one-loop partition functions around each topological sector on $M/\mathbb{Z}_h$ and $B$ explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on $B$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_02313 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone) Lundin, Jim Mauch, Roman Ruggeri, Lorenzo High Energy Physics - Theory We compute the Coulomb branch partition function of the 4d $\mathcal{N}=2$ vector multiplet on closed simply-connected quasi-toric manifolds $B$. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is to obtain flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $\mathcal{N}=1$ vector multiplet on closed simply-connected toric Sasaki-manifolds $M$ which are principal $S^1$-bundles over $B$. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients $M/\mathbb{Z}_h$ along the $S^1$, the locus picks up non-trivial flat connections which, in the limit $h\to\infty$, provide the sought-after fluxes on $B$. We compute the one-loop partition functions around each topological sector on $M/\mathbb{Z}_h$ and $B$ explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on $B$. |
| title | From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone) |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2305.02313 |