From 5d flat connections to 4d fluxes (the art of slicing the cone)

DOI10.1007/JHEP10(2023)155arXiv2305.02313OpenAlexW4388203049MaRDI QIDQ6083852

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Publication date: 8 December 2023

Published in: (Search for Journal in Brave)

Abstract: We compute the Coulomb branch partition function of the 4d $mathcalN=2$ 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 obtaining flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d $mathcalN=1$ 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 $hoinfty$, 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 $B$.

Full work available at URL: https://arxiv.org/abs/2305.02313

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